The Interior — SkateboardingGrades 11–12

Unit 14 · Engineering the Board and the Ramp

Start with the story. Then go through each chapter, one lesson at a time. Each lesson has three short checks. Each chapter ends with a review. The unit ends with a wrap-up.

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14Unit

Engineering the Board and the Ramp

Science

A skateboard looks simple: a board, two trucks, four wheels. Look closer and every part is an engineering decision. Seven thin plies of maple are glued and pressed into a curve. Wheels are cast from liquid chemicals and rated with a hardness gauge. Eight small steel bearings let those wheels spin thousands of times a minute. Ramps are curves drawn from circles, and their radius decides how hard a rider's legs must work.

This unit follows the engineer's way of thinking. You will see how layered wood and concave make a deck stiff without making it heavy, why a soft wheel wins on a rough street and loses at a smooth park, and why the ABEC number on a bearing box is about precision, not speed. Then you will design a ramp: use geometry to find its top angle and footprint, energy to predict a rider's speed, and centripetal acceleration to predict how heavy the rider will feel at the bottom.

By the end you will be able to explain the trade-offs behind a skateboard setup, read wheel and bearing labels correctly, and carry out a full ramp design calculation with each step shown. You will also know how ramps are framed and built safely, and how to check a design against the people who will ride it.

When it happened
1687

Isaac Newton publishes the Principia, with the laws of motion used to study ramps today

c. 1959

Store-made skateboards appear in California

1963

Larry Stevenson starts selling Makaha skateboards

1971

Larry Stevenson's kicktail patent is granted

Early 1970s

Frank Nasworthy's Cadillac Wheels bring urethane to skateboarding

Mid-1970s

Sealed precision bearings come into use on skateboards

1976

Carlsbad Skatepark in California and Skateboard City in Florida open

1976–77

A California drought leaves empty pools that skaters ride as transitions

1990

Skaters begin building Burnside skatepark under a Portland, Oregon, bridge

2002

The Tony Hawk Foundation starts helping communities build public skateparks

2020

The Tony Hawk Foundation is renamed The Skatepark Project

Chapter

Decks, Wheels and Bearings

Engineering
Big questionHow do engineers choose the wood, urethane and steel in a skateboard, and what does each choice give up?
The story

The Thumbnail Test

A shop worker uses one thumb to show why two wheels that look alike ride so differently.

A customer named Dani walks into a small skate shop with a cracked deck under one arm. She wants to build a new board for the concrete park across town. On the glass counter sit two sets of wheels. Both are white. Both are 54 millimeters across. To Dani they look exactly the same.

The shop worker, Marcus, picks up one wheel and presses his thumbnail hard into the riding surface. A small crescent-shaped dent appears and then slowly fades. He does the same to the second wheel. His nail barely marks it. "This one is 85A," he says, tapping the first. "This one is 99A. Same size, same color, very different ride."

He explains that the softer wheel squashes a little over cracks and pebbles. It grips the ground and smooths out the bumps on an old sidewalk. The harder wheel barely changes shape. On smooth park concrete it keeps more of its speed, and it slides when a skater wants it to. Dani realizes she has to decide where she will ride before she decides what to buy.

Then Marcus turns to the wall of decks. He flexes one between his hands and points to the stripes along its edge. "Seven layers of maple," he says. "Glued and pressed into this curve." He spins a wheel on a display truck, and it keeps turning for a long time. "And that is the bearings. Every part of this board is a choice somebody made."

Talk about itIf you could only buy one set of wheels for both a rough street and a smooth park, how would you decide on the hardness?
Section 1

The Deck

27.1

Seven Thin Layers of Maple

Main ideaMost decks are seven thin plies of hard maple glued together and pressed in a mold, which makes them strong, light and springy.

Look at the edge of almost any skateboard deck and you will see thin stripes. Each stripe is a , a sheet of wood usually under 2 millimeters thick. Most decks use seven plies of hard maple, a dense wood that grows in the northern United States and Canada. Stacked together, seven plies make a deck roughly 11 to 12 millimeters thick. That is thin enough to stay light and thick enough to survive landings.

The plies are not all laid the same way. Wood is strongest along its , the direction its fibers run. Most plies run with the grain along the board’s length, which resists bending from nose to tail. One or more plies run across the board. These cross layers stop the deck from splitting along the grain when a wheel or tail strikes hard. Builders call this a : thin layers glued so their strengths add up.

First, workers spread glue on each ply. Next, they stack the plies in order and set the stack in a mold shaped like the finished board. Then a hydraulic press squeezes the stack, and it stays under pressure while the glue sets. The mold gives the deck its upturned nose and tail and its curve from side to side. Finally, the pressed blank is cut to shape, drilled for the trucks, sanded and given a graphic.

Early boards from the 1960s were often a single plank of solid wood. A single plank can split along its grain and warp when it gets wet. Layered maple became the common choice because a laminate spreads stress across many glue lines. Some modern decks add layers of fiberglass, carbon fiber or bamboo, but seven-ply maple remains the most common recipe.

Words to know
ply
one thin sheet of wood in a layered deck; most decks have seven
grain
the direction the wood's fibers run; wood is strongest along it
laminate
a material made of thin layers glued together so their strengths combine
Check yourself

1. What is a ply in a skateboard deck?

2. Why do one or more plies run across the board instead of along it?

3. Which step comes right after the glued plies are stacked?

27.2

Concave and Stiffness

Main ideaBending a deck into a side-to-side curve called concave makes it much stiffer and gives the feet edges to press against.

Hold a metal tape measure flat and push it out from the case. It droops after a short distance. Now let it curl into its normal curved shape. It can stick straight out much farther. The metal did not change. Only its cross-section, the shape you would see if you sliced it across, changed. A skateboard deck uses the same trick.

is the gentle side-to-side curve pressed into a deck, with the edges higher than the middle. Engineers describe a shape’s resistance to bending with the . The farther material sits from the bending line through the middle of the cross-section, the larger this number and the stiffer the part. Curving the deck moves its edges up and away from that line. The same seven plies become stiffer without adding any weight.

Concave also helps the feet. The raised edges, called rails, give the toes and heels something to press and catch. When a skater flicks off the toe-side edge for a kickflip, the curve guides where the foot leaves the board. Steep concave locks the feet in place. Mellow concave feels flatter and more open, and some skaters find it easier to stand on for long rides.

Stiffness also grows quickly with thickness. For a flat strip, stiffness rises with the cube of its thickness. A deck that is 10 percent thicker is about 1.1 × 1.1 × 1.1 = 1.33 times as stiff, a third stiffer. It is also about 10 percent heavier. Concave lets a maker gain stiffness without paying that weight cost.

Words to know
concave
the side-to-side curve in a deck, with the edges higher than the middle
second moment of area
a number engineers use for how a cross-section's shape resists bending; material far from the middle raises it
rails
the long side edges of a deck
Check yourself

1. What does concave do to a deck's stiffness?

2. A flat strip is made 10 percent thicker. About how much stiffer does it get?

3. Why does a curled tape measure stick out farther than a flat one?

27.3

Nose, Tail and Wheelbase

Main ideaThe kicked-up tail and nose make levers for tricks, and the wheelbase sets how stable or quick a board feels.

Larry Stevenson of Makaha received a patent for the in 1971. A kicktail is the upturned end of a deck. Pressing it lifts the front wheels like a seesaw, so a skater can turn sharply or pop the board into the air. Modern decks have a kick at both ends. The two ends are often shaped a little differently so a skater can tell the nose from the tail without looking.

The tail works as a lever. The back truck’s axle is the pivot. When the back foot pushes down on the tail, the rest of the board swings up around that axle. A longer, steeper tail gives the foot more distance from the pivot and lets it strike the ground sooner. A short, flat tail needs a bigger stomp to get the same lift.

The is the distance between the two trucks, usually measured between the inner mounting holes. A longer wheelbase spreads the wheels apart. The board feels steadier at speed and turns in wider arcs. A shorter wheelbase makes quick turns and spins easier but feels twitchier going fast. Many street decks have a wheelbase of about 35 to 37 centimeters, and longboards stretch much longer.

Width matters too. Many street and park decks today are about 20 to 22 centimeters wide. A wider deck gives bigger feet more room and more stability on landings. A narrower deck is lighter and easier to flip. A skater with large shoes on a narrow deck may catch the toes or heels on tricks. The best width is the one that fits the rider’s feet and style.

Words to know
kicktail
the upturned end of a deck that lets a skater lift the wheels; Larry Stevenson's patent was granted in 1971
wheelbase
the distance between the front and back trucks
pivot
the point a lever turns around; for an ollie, the back axle
Check yourself

1. In 1971, who received a patent for the kicktail?

2. When the back foot presses the tail, what does the board pivot around?

3. What does a longer wheelbase usually give a board?

Section 2

Wheels

27.4

Measuring Wheel Hardness

Main ideaWheel hardness is measured on the durometer A scale, from about 78A for soft wheels to about 101A for hard ones.

A is a small gauge that measures how hard a material is. It presses a spring-loaded pin, called an indenter, into the surface. A soft material lets the pin sink in, so the gauge reads low. A hard material pushes back, so the gauge reads high. Skate wheels are rated on the Shore A scale, written as a number followed by A, such as 85A.

Skate wheels run from about 78A to about 101A. Wheels around 78A to 87A are soft. They feel cushy, grip well and roll quietly over rough pavement. Wheels around 88A to 95A are in the middle. Wheels around 96A to 101A are hard. They are built for smooth skatepark concrete, wood ramps and street spots with smooth ground. The scale is not a straight line of feel, so a few points near the hard end can feel like a big change.

The A scale tops out at 100, and readings near the top are less precise. For that reason some wheel makers rate very hard wheels on a B scale. The B scale uses a different indenter and reads about 20 points lower than A for the same wheel. An 83B wheel is roughly a 103A wheel. If two labels use different letters, the numbers cannot be compared directly.

Marcus’s thumbnail trick from the shop is a rough version of a durometer. The softer wheel let his nail sink in and then slowly recovered. The harder wheel barely took a mark. A real gauge removes the guesswork by using the same pin and the same spring every time.

Words to know
durometer
a gauge that measures hardness by pressing a spring-loaded pin into a material
Shore A scale
the hardness scale used for most skate wheels, written like 85A or 99A
indenter
the pin in a durometer that presses into the material
Check yourself

1. How does a durometer measure hardness?

2. Which wheel is softest?

3. Why can't you directly compare an 83B wheel with an 83A wheel?

27.5

Soft Wheels, Hard Wheels

Main ideaSoft wheels squash to grip and smooth rough ground; hard wheels keep their shape to roll fast and slide on smooth surfaces.

Every wheel flattens a little where it touches the ground. That flat spot is the . A soft wheel flattens more, so its contact patch is larger. A larger patch gives more grip in turns and spreads small bumps over a wider area, so the rider feels less shaking. A hard wheel flattens less. Its small patch grips less and lets the wheel slide more easily.

Squashing a wheel takes energy, and the urethane does not give all of it back as it springs into shape. The lost part turns into a little heat. This loss is called . On smooth concrete, a soft wheel keeps squashing and recovering with every turn, so it loses more energy than a hard wheel. That is one reason hard wheels feel faster at a skatepark. On rough ground the picture flips: a hard wheel bounces off every pebble while a soft wheel rolls over them.

Hard wheels are also chosen for slides. In a powerslide, the skater turns the board sideways and skids the wheels to slow down. A hard wheel breaks loose smoothly and slides. A soft wheel grips so well that it can stop suddenly and throw the rider forward. On a ledge or a smooth park, skaters who want to slide or land a sideways trick often pick wheels in the high 90s.

Grip and speed pull against each other. A commuter on old sidewalks values a quiet, smooth ride, so a soft wheel wins. A park skater values speed and slides on smooth ground, so a hard wheel wins. Many skaters who ride both pick something in the middle, around 90A to 95A, and accept a little of each problem.

Words to know
contact patch
the small flattened area where a wheel touches the ground
hysteresis
energy lost as heat when a material squashes and springs back
powerslide
turning the board sideways and skidding the wheels to slow down
Check yourself

1. Why does a soft wheel grip better?

2. What is hysteresis in a wheel?

3. A skater wants to do powerslides at a smooth park. Which wheel fits best?

27.6

Wheel Size

Main ideaBigger wheels roll over cracks and hold speed; smaller wheels are lighter and lower, which helps flip tricks.

Wheel diameter is measured in millimeters across the wheel. Many street wheels are about 50 to 54 millimeters. Many park and transition wheels are about 54 to 60. Cruiser wheels are often 60 millimeters or larger. A larger wheel meets a crack at a gentler angle, so the crack is less likely to stop it. That is why cruisers and longboards use big wheels.

Smaller wheels have their own strengths. They weigh less, so the whole board is lighter to pop and flip. They also sit the deck closer to the ground, which some street skaters like for flip tricks and ledges. A larger wheel carries its momentum longer, which helps on a big bowl but adds weight to every ollie.

Large wheels bring one problem. In a sharp turn the deck tilts toward the wheel. If the wheel is big and the trucks are loose, the wheel can touch the bottom of the deck. This is . It stops the wheel instantly and can throw the rider. Builders prevent it by tightening the trucks a little, choosing a smaller wheel or adding a , a thin plastic spacer between the truck and the deck.

Diameter also sets how fast the wheel must spin. One turn of a wheel rolls the board one circumference forward, which is π times the diameter. A 54 mm wheel has a circumference of π × 0.054 m = 0.170 m. At 5 meters per second, about a fast jog, it turns 5 ÷ 0.170 = 29.4 times every second. That is about 1,760 turns per minute, which is why bearings matter.

Words to know
diameter
the distance straight across a wheel through its center, measured in millimeters
wheel bite
when a wheel touches the bottom of the deck in a turn and stops suddenly
riser pad
a thin spacer between the truck and the deck that lifts the deck higher
Check yourself

1. Why do cruiser boards often use large wheels?

2. What is wheel bite?

3. A 54 mm wheel has a circumference of 0.170 m. How many turns per second does it make at 3.4 m/s?

27.7

What Urethane Is

Main ideaUrethane wheels are cast from two liquids that react into a tough, elastic plastic, and changing the recipe changes the hardness.

In the early 1960s many skateboards rolled on steel wheels or on clay composite wheels borrowed from roller skates. Steel wheels skidded on small stones and shook the rider. Clay wheels wore quickly and grabbed poorly. In the early 1970s Frank Nasworthy began selling urethane wheels under the name Cadillac Wheels. The new wheels gripped and rolled smoothly, and they helped start skateboarding’s second boom.

, usually shortened to urethane, is a . A polymer is a material made of very long chain molecules built from many small repeating pieces. To make a wheel, a factory mixes two liquids. One is called a polyol and the other an isocyanate. When they meet, they react and link into long chains that also tie to one another. The liquid becomes a solid that is tough and springy.

Wheels are usually . The mixed liquid is poured into a mold around a core or hub, then cured with time and heat until it hardens. After curing, the wheel is trimmed and its riding surface is cut smooth on a lathe. The chemist can change the hardness by changing the mix. More tightly linked chains give a harder wheel. Looser chains give a softer, more elastic one.

Urethane suits wheels because it resists scraping and tearing better than rubber and stays springy over a wide range of temperatures. It wears slowly, but it does wear. A wheel used for many powerslides can develop a flat spot, a worn patch that makes the wheel thump on every turn. Rotating wheels to new positions helps them wear more evenly.

Words to know
polyurethane
a tough, springy plastic used for skate wheels; often called urethane
polymer
a material made of very long chain molecules built from small repeating pieces
cast
made by pouring a liquid into a mold and letting it harden
Check yourself

1. Who began selling urethane skateboard wheels as Cadillac Wheels in the early 1970s?

2. What is a polymer?

3. How can a chemist make a urethane wheel harder?

Section 3

Bearings

27.8

How a Ball Bearing Works

Main ideaBearings replace sliding with rolling, so a wheel spins on its axle with very little friction.

A skateboard wheel turns around a steel axle that does not move. If the wheel’s hole simply rubbed on the axle, sliding friction would slow it and wear both parts. A fixes this. A skateboard bearing is a ring of small steel or ceramic balls held between two steel rings, called races. The inner race sits on the axle and stays still. The outer race presses into the wheel and turns with it.

The balls roll instead of slide. Rolling friction is far smaller than sliding friction. For example, two dry steel parts sliding on each other might have a friction coefficient around 0.5, while a well-made ball bearing acts more like 0.001 to 0.005. A thin film of grease or oil, called , lowers it further and keeps the metal from wearing. A cage holds the balls evenly spaced so they do not rub against each other.

Almost every skateboard uses the same bearing size, called the 608. It has an 8 millimeter hole, a 22 millimeter outside diameter and a 7 millimeter width. Each wheel takes two bearings, one pressed into each side, so a board has eight. A small metal tube called a spacer can sit between the two bearings inside the wheel so that tightening the axle nut does not squeeze them sideways.

cover the sides of the bearing to keep out dirt and water. Some are thin metal; others are rubber seals that block more grit but add a little drag. Dirt is a bearing’s worst enemy. One grain of sand between a ball and a race acts like a speed bump on every turn.

Words to know
bearing
a ring of balls between two races that lets a wheel spin on an axle with little friction
lubricant
grease or oil that lowers friction and wear between moving parts
shields
covers on the sides of a bearing that keep dirt and water out
Check yourself

1. In a skateboard bearing, which part turns with the wheel?

2. How many bearings does a full skateboard usually have?

3. Why do bearings lower friction?

27.9

ABEC Is Precision, Not Speed

Main ideaThe ABEC scale rates how precisely a bearing is made, not how fast a skateboard will roll.

Bearing boxes often print a big number: ABEC 3, ABEC 5, ABEC 7. Many buyers think a higher number means a faster board. It does not. stands for the Annular Bearing Engineering Committee, part of the American Bearing Manufacturers Association. Its scale uses odd numbers, 1, 3, 5, 7 and 9. Each step sets a tighter .

A tolerance is how far a real part may differ from its design size. If a bearing’s hole is designed to be 8 millimeters, a tolerance says how much bigger or smaller it may be and still pass. A higher ABEC grade allows smaller errors in the hole, the outside diameter and how true the rings run. Those tight tolerances matter in machines that spin thousands of times a minute for hours, such as precision tools.

The ABEC scale does not rate the things that matter most on a skateboard. It says nothing about the steel’s toughness, the quality of the balls, the lubricant, the shields or how the bearing handles side loads. A skateboard bearing takes hard sideways hits on every landing and every turn, which precision machines rarely feel. A well-made bearing with a low ABEC number can roll as well as or better than a poorly made one with a high number.

A board’s speed comes mostly from the rider’s push and the hill, the wheels and the ground, and how clean the bearings are. A clean, lightly lubricated ABEC 3 bearing will outroll a dirty ABEC 9. Some skate companies skip ABEC ratings and test bearings in their own ways for skateboard loads.

Words to know
ABEC
a scale from the Annular Bearing Engineering Committee that rates how precisely a bearing is made
tolerance
how far a real part may differ from its design size and still pass
precision
how closely a made part matches its design size and shape
Check yourself

1. What does a higher ABEC number mean?

2. Which is NOT rated by the ABEC scale?

3. Which bearing will most likely roll better on a skateboard?

27.10

Keeping Bearings Rolling

Main ideaBearings roll best when they are clean, lightly lubricated and not squeezed by an overtightened axle nut.

The axle nut holds the wheel on the truck. If it is too loose, the wheel wobbles and rattles. If it is too tight, it squeezes the bearings sideways and the wheel slows down. First, tighten the nut until it touches the speed washer. Next, back it off a small amount. Then spin the wheel. It should turn freely with only a tiny side-to-side play. Built-in spacers or speed rings help hold this setting.

Water and grit cause most bearing trouble. Riding through puddles can rust the races and balls. Rust makes a gritty, grinding sound and a wheel that stops quickly when spun. If a board gets wet, dry it and spin the wheels before storing it. A bearing that grinds even when clean is worn and should be replaced. Bearings are inexpensive compared with an injury from a wheel that locks up.

To clean bearings, a skater removes the wheels, pries or presses the bearings out with a bearing tool or the truck axle, and gently removes the shields if the design allows. They wash out old grease and dirt with a cleaner the bearing maker recommends, dry the bearings completely and add a few drops of skate lubricant. Too much lubricant attracts more dirt. Working at a table with a towel catches tiny parts and keeps the balls out of the carpet.

Skaters can test a bearing with a spin. Hold the board upside down and flick a wheel. A healthy bearing spins smoothly and quietly and slows gradually. A wheel that stops in a second or two, grinds or wobbles is telling you something. Checking the axle nuts and spins before a session is a fast safety habit.

Words to know
axle nut
the nut that holds the wheel on the truck's axle
speed washer
a thin metal ring between the bearing and the axle nut or truck
rust
damage to steel caused by water and air, which makes bearings grind
Check yourself

1. What happens if the axle nut is tightened too much?

2. Why should a skater avoid adding too much lubricant?

3. A wheel grinds and stops quickly even after cleaning. What is the best choice?

Section 4

Engineering Trade-Offs

27.11

No Part Is Best at Everything

Main ideaEvery skateboard part trades one strength for another, so engineers start from where and how the board will be ridden.

Engineers call the conditions a design must meet its . A park board must survive hard landings and roll fast on smooth concrete. A commuter board must glide over cracks and stay quiet. A street board must be light enough to flip. The limits they cannot change, like cost, weight or the size of a rider’s foot, are . The best design is the one that fits the job.

Each choice gains something and gives something up. This is a . A thicker deck is stiffer and stronger but heavier. A wider deck is steadier but harder to flip. A soft wheel grips and smooths rough ground but feels slower on smooth concrete. A big wheel rolls over cracks but adds weight and risks wheel bite. Rubber seals keep out grit but add a little drag.

Here is a worked example. A deck goes from seven plies to eight, so it becomes 8 ÷ 7 = 1.14 times as thick, about 14 percent thicker. Its stiffness rises by 1.14 × 1.14 × 1.14 = 1.49, about 49 percent. Its weight also rises by about 14 percent. A maker deciding whether that trade is worth it would ask who rides the board. A heavy rider on big ramps might want the stiffness. A street skater flipping the board all day might not.

Good engineering also tests the guesses. A maker can bend sample decks with a known weight and measure how far they sag, drop them onto concrete again and again, or ride them for weeks and look for cracks. Results lead to changes, and the changes are tested again. This loop of design, test and improve is how boards changed from planks in the 1960s to the shaped laminates of today.

Words to know
requirements
the conditions a design must meet to do its job
constraints
limits a design cannot change, such as cost, weight or size
trade-off
a choice that gains one strength by giving up another
Check yourself

1. What is a trade-off in design?

2. A deck goes from 7 to 8 plies. About how much stiffer does it get?

3. Which is a constraint rather than a requirement?

27.12

Matching a Setup to the Ground

Main ideaA good setup matches deck, wheels and bearings to the ground and the kind of riding the skater plans to do.

Start with the ground. Smooth skatepark concrete or wood ramps reward hard wheels, around 95A to 101A, because they keep their speed and slide when needed. Rough streets, old sidewalks and outdoor courts reward softer wheels, around 78A to 90A, because they absorb bumps and grip. A skater who rides both can split the difference in the low 90s.

Next, pick a size. Street and flat-ground tricks favor smaller wheels, about 50 to 54 millimeters, and a deck that fits the feet without extra weight. Bowls and ramps favor slightly bigger wheels, about 54 to 60 millimeters, and often a wider deck for steady landings at speed. A cruiser for getting around may use wheels of 60 millimeters or more, with riser pads to prevent wheel bite.

Then think about the rider. A tall rider with large feet may want a wider deck so the toes and heels do not hang far over the rails. A beginner often feels safer on a wider, steadier board with medium wheels. Comfort and confidence help a learner practice more, and practice matters more than any part.

Safety comes with every setup. Before riding, check that the axle nuts are on, the wheels spin freely and the trucks are tight enough to stop wheel bite. Then put on a helmet that fits and is buckled, plus wrist guards and pads while learning. A board tuned for the ground is easier to control, and control is what keeps a session safe.

Words to know
setup
the combination of deck, trucks, wheels and bearings on one board
cruiser
a board built for riding around town, usually with large soft wheels
transition
the curved part of a ramp or bowl between the flat ground and the wall
Check yourself

1. Which wheels fit a rider who skates a smooth concrete bowl?

2. Why might a cruiser board need riser pads?

3. What should a skater check on the board before riding?

Chapter review

Decks, Wheels and Bearings

0 / 8

1. How many plies of maple do most skateboard decks use?

2. What does concave add to a deck?

3. Which wheel hardness best fits rough, cracked sidewalks?

4. What does a durometer measure?

5. What does the ABEC scale rate?

6. What are urethane wheels made from?

7. A 60 mm wheel has a circumference of 0.188 m. About how many turns per second does it make at 5 m/s?

8. Why do hard wheels often feel faster on smooth park concrete?

Chapter

Ramps by Design

Engineering
Big questionHow can the shape of a curve be chosen with physics so a ramp is fun, safe and right for the people who ride it?
The story

Two Curves on the Table

A youth club must choose between two ramp plans that look almost the same from above.

On a folding table in a community center, two ramp plans lie side by side. Both are mini ramps 1.2 meters tall. Both have a flat stretch in the middle and a platform at each end. A volunteer named Teresa, who has built ramps for years, has drawn both. She asks the club's teenagers to pick one.

The first plan has a tight curve. Its transition is drawn from a circle with a radius of 1.5 meters. The ramp is short and fits easily in the small lot behind the building. The second plan uses a wide curve with a radius of 2.5 meters. It is longer, needs more plywood and stretches nearly to the fence.

A skater named Jalen likes the tight curve. "It looks steeper," he says. "More exciting." A younger rider named Ana frowns. She has felt a tight ramp before. "At the bottom it squishes you," she says. "Your knees fold if you are not ready." Teresa smiles and takes out a calculator.

"Ana felt something real," she says. "We can measure it before we buy a single board." She writes two lines on the plan: the speed a rider will have at the bottom, and how heavy the rider will feel there. The numbers for the two curves are not the same. The group leans in to see why.

Talk about itWithout doing any math yet, which curve do you think will make riders feel heavier at the bottom, and why?
Section 1

The Shape of a Transition

28.1

A Curve From a Circle

Main ideaMost ramp transitions are arcs cut from a circle, and the circle's radius sets how tight or mellow the curve feels.

A is the curved surface that joins flat ground to the wall of a ramp. Skaters often call it tranny, and riding ramps and bowls is called transition skating. The first transitions people skated were the curved walls of empty backyard swimming pools during the California drought of 1976 and 1977. Builders later copied those curves in wood and concrete.

Most ramp builders draw a transition as part of a circle. The is the distance from the circle’s center to its edge. A quarterpipe uses one quarter of a circle or less. If the curve runs a full quarter, from flat to straight up, the ramp’s height equals the radius. A circle with a 1.5 meter radius makes a curve that reaches vertical 1.5 meters off the ground.

A small radius makes a tight curve. The rider turns from flat to steep in a short distance. A large radius makes a wide, mellow curve. The rider turns more gradually and has more room to react. Two ramps of the same height can feel completely different because their radii differ.

A ramp does not have to reach vertical. A mini ramp often stops before the curve gets straight up, so its top edge is steep but still tilted. A vert ramp continues the curve to vertical and then adds a short straight-up section on top. Vert ramps are usually more than 3 meters tall and are for experienced riders.

Words to know
transition
the curved surface that joins flat ground to the wall of a ramp or bowl
radius
the distance from the center of a circle to its edge; it sets how tight a transition is
quarterpipe
a single ramp whose curve is part of a quarter circle
vert ramp
a tall ramp whose curve reaches straight up, with a vertical section on top
Check yourself

1. What is a transition?

2. A quarterpipe's curve runs a full quarter circle from flat to vertical. Its radius is 2 meters. How tall is the curve?

3. Which ramp has the tighter curve?

28.2

How Steep Is the Top?

Main ideaIf a ramp stops before vertical, geometry tells you how steep its top edge is and how long the curve runs along the ground.

A curve cut from a circle rises slowly at first and then faster. The height reached after the curve turns through an angle θ is h = r(1 − cos θ). Here r is the radius and θ is measured from flat ground. At θ = 90 degrees, cos θ is 0, so the height is the full radius. That is a vertical wall.

Here is a worked example. A builder wants a ramp 1.2 meters tall using a radius of 1.8 meters. First, divide: 1.2 ÷ 1.8 = 0.667. Next, solve 1 − cos θ = 0.667, so cos θ = 0.333. Then find the angle whose cosine is 0.333, which is about 70.5 degrees. The top edge of this ramp tilts at about 70 degrees from flat, steep but not vertical.

The same circle tells how long the curve runs along the ground. The horizontal length is r × sin θ. For this ramp it is 1.8 × sin 70.5° = 1.8 × 0.943 = 1.70 meters. The builder now knows that each side of the ramp needs about 1.7 meters of floor space for the curve alone, before adding any flat bottom or platform.

These two numbers, the top angle and the floor length, guide most design choices. A larger radius at the same height gives a gentler top angle but a longer footprint. A smaller radius gives a steeper top in less space. Space, budget and the riders’ skill decide which way to go.

Words to know
angle
the amount a line or surface turns, measured in degrees; flat is 0 and straight up is 90
footprint
the area of ground a ramp covers
cosine
a ratio from geometry that links an angle to the sides of a right triangle; used to find how high a curve rises
Check yourself

1. For a curve with radius r turning through angle θ, which formula gives its height?

2. A ramp is 1.2 m tall with a 2.4 m radius. What is cos θ at the top?

3. Keeping the height the same, what does a larger radius do?

28.3

Coping, Platform and Flat Bottom

Main ideaThe coping, the platform and the flat bottom each give riders something they need: a grinding edge, a safe place to start and time between walls.

The is the edge at the top of a transition. On a wooden ramp it is usually a round steel pipe fixed so it sticks out just past the riding surface. In a concrete pool or bowl it is often a row of stone or concrete blocks, a reminder of the backyard pools where skaters first rode it. Coping gives the trucks a hard, smooth edge to grind and gives the rider a clear signal that the wall has ended.

Behind the coping sits the , a flat deck where riders stand, wait their turn and start runs. A platform needs room to stand with a board and to step back safely. On taller ramps, a guardrail along the back keeps people from stepping off the edge. Riders set the tail on the coping here before dropping in.

The is the level stretch between two transitions on a halfpipe. Without it, a rider would go from one curve straight into the next. A flat bottom gives a moment to settle, shift the feet and get ready for the next wall. Ignoring friction, it does not change the rider’s speed, because a level surface neither raises nor lowers them. It does add length, cost and time.

A mini ramp for a youth club might have a flat bottom a few meters long. Too short and the walls come too fast. Too long and riders lose speed to friction before reaching the other side. Builders choose a length that fits the riders and the space, then mark it on the plan before cutting any wood.

Words to know
coping
the edge at the top of a transition, often a steel pipe or stone blocks, used for grinds
platform
the flat deck at the top of a ramp where riders stand and start runs
flat bottom
the level stretch between two transitions on a halfpipe
Check yourself

1. What is the coping on a wooden ramp usually made of?

2. Ignoring friction, what does a flat bottom do to a rider's speed?

3. Why do taller ramps have a guardrail on the platform?

Section 2

Energy on the Ramp

28.4

Height Becomes Speed

Main ideaAs a rider drops down a transition, potential energy turns into kinetic energy, so the drop height predicts the speed at the bottom.

A rider standing at the coping of a 1.2 meter ramp has stored energy because of height. This is , equal to mgh: mass times g times height. For a 60 kilogram rider, it is 60 × 9.8 × 1.2 = 705.6 joules. A joule is the SI unit of energy, about the energy needed to lift a small apple one meter.

As the rider drops in, height turns into motion. Motion energy is , equal to ½mv². If no energy were lost, all 705.6 joules would become kinetic energy at the bottom. Setting mgh = ½mv² and cancelling the mass gives v = √(2gh). The mass cancels, so a light rider and a heavy rider reach the same speed in this ideal case.

Work it through. With h = 1.2 m, v = √(2 × 9.8 × 1.2) = √23.52 = 4.85 meters per second. That is about 17 kilometers per hour. The shape of the curve does not change this answer. A tight curve and a wide curve of the same height give the same ideal speed at the bottom, because only the height drop counts.

The same idea runs backward. A rider moving at 4.85 meters per second at the bottom can, with no losses, coast up to 1.2 meters on the other wall. The rule of says energy is not created or destroyed; it changes form. This is why a rider rolling back and forth can predict how high each wall will carry them.

Words to know
potential energy
stored energy from height, equal to mass × g × height (mgh)
kinetic energy
energy of motion, equal to one half × mass × speed squared
conservation of energy
the rule that energy is not created or destroyed, only changed in form
Check yourself

1. A 50 kg rider stands at the top of a 1.0 m ramp. What is the potential energy?

2. Why do a light rider and a heavy rider reach the same ideal speed at the bottom?

3. Two ramps are the same height but one has a tighter curve. With no friction, which gives more speed at the bottom?

28.5

Losses and Pumping

Main ideaFriction and air drain energy on every pass, and riders replace it by pumping: crouching high and pressing up through the bottom of the curve.

In real life a rider never quite reaches the starting height on the next wall. Rolling resistance in the wheels, friction in the bearings and air pushing on the body turn some energy into heat. Suppose a 60 kilogram rider drops from 1.2 meters and coasts up only 1.0 meter on the other side. The energy lost is mg times the difference: 60 × 9.8 × 0.2 = 117.6 joules, about one sixth of the 705.6 joules they started with.

Riders make up for the loss without pushing off the ground. They . First, the rider stays low in a crouch as the board rolls down from the top of the wall. Next, as the board passes through the bottom of the curve, the rider presses up through the legs and stands taller. Then they crouch again near the top of the next wall. Done well, each pass climbs a little higher.

Pumping works because the rider pushes hardest where the ramp pushes back hardest. At the bottom of the curve the board presses up with extra force, so standing up there takes more work than it gives back when the rider crouches near the top, where the push is weaker. The extra work becomes extra energy. A child on a swing adds energy in a similar way by moving their body at the right moments.

A common problem is pumping on the flat bottom instead of the curve. Standing up on flat ground adds nothing, because the floor pushes back only with normal body weight. Another problem is leaning back on the wall, which makes the board shoot out. The fix is to keep the shoulders over the board, square to the ramp surface, and to save the push for the curve.

Words to know
pump
to gain speed on a ramp by crouching and then pressing up through the legs at the bottom of the curve
rolling resistance
the drag that slows a rolling wheel as it squashes against the ground
joule
the SI unit of energy
Check yourself

1. A 60 kg rider drops from 1.0 m and only reaches 0.8 m on the next wall. How much energy was lost?

2. When does a rider press up through the legs to pump?

3. A rider keeps leaning back on the wall and the board shoots out. What helps?

28.6

Dropping In With Energy in Mind

Main ideaDropping in turns a standing rider's height into speed, and committing the front foot keeps the board under the body.

Dropping in means starting a run from the top of a ramp instead of rolling in from the flat. It is the moment when the most potential energy turns into motion. Learn it on a small ramp, with a helmet that fits and is buckled, wrist guards and knee pads, and with a friend or coach nearby. Many learners first practice by rolling up a ramp and riding back down fakie, so they know the feel of the curve.

First, set the tail on the coping with the back wheels hooked behind it and the back foot on the tail. Next, put the front foot over the front bolts. Then lean forward and press the front foot down firmly, so the front wheels touch the ramp and the body moves with the board. The board drops and rolls away, and the rider rides it down in a low, balanced crouch.

The physics explains the most common problem. If the rider leans back, the board accelerates down the slope but the body stays behind at the top. The board shoots ahead and the rider falls backward. Committing the front foot keeps the body’s center of mass over the board as both speed up together.

Falling small is part of learning. If a drop-in goes wrong, crouch low, let the knee pads touch first and slide down the transition on them. Do not reach back with locked straight arms, which is how many wrist injuries happen. Fear before a drop-in is a normal signal. Breaking the move into smaller steps, such as practicing on a lower ramp, helps it shrink.

Words to know
drop in
to start a run from the coping at the top of a ramp
fakie
rolling backward while standing in your normal stance
center of mass
the point where an object's mass is balanced; for a rider, near the hips
Check yourself

1. Where does the back foot go to set up a drop-in?

2. Why does leaning back cause a fall on a drop-in?

3. What is the safer way to fall on a ramp?

Section 3

Forces in the Curve

28.7

Why Riders Feel Heavier

Main ideaAt the bottom of a curve, the ramp must push up extra hard to bend the rider's path, so the rider feels heavier.

Anything moving in a circle is accelerating toward the circle’s center, even at a steady speed, because its direction keeps changing. This is , and it equals v²/r: speed squared divided by the radius. At the bottom of a transition, the center of the circle is above the rider. So the ramp must push up harder than usual to curve their path upward.

The upward push of a surface is the . On flat ground it equals body weight, mg. At the bottom of the curve, Newton’s second law gives N − mg = mv²/r, so N = m(g + v²/r). The rider’s legs feel that larger force. Riders sometimes describe it as the ramp squishing them, which is what Ana felt in the story.

Work it through for a 60 kilogram rider who drops in from 1.2 meters on a curve with a 2.0 meter radius. The speed at the bottom is 4.85 meters per second, so v² = 23.52. Then v²/r = 23.52 ÷ 2.0 = 11.76 m/s². The normal force is 60 × (9.8 + 11.76) = 60 × 21.56 = 1,293.6 newtons. Body weight is 60 × 9.8 = 588 newtons, so the rider feels about 2.2 times as heavy.

There is a shortcut. Because v² = 2gh after a drop from height h, the felt weight at the bottom is 1 + 2h ÷ r times normal. For the 1.2 meter drop on a 2.0 meter radius, that is 1 + 2.4 ÷ 2.0 = 2.2. If the drop height equals the radius, the rider feels three times as heavy. This simple model treats the rider as a point and ignores friction.

Words to know
centripetal acceleration
the acceleration toward the center of a curve, equal to speed squared ÷ radius (v²/r)
normal force
the push of a surface straight out from it, against whatever presses on it
newton
the SI unit of force
Check yourself

1. What is the formula for centripetal acceleration?

2. A rider moves at 4 m/s at the bottom of a curve with a 2 m radius. What is the centripetal acceleration?

3. Why does a rider feel heavier at the bottom of a transition?

28.8

Why Tight Curves Feel Harder

Main ideaA tighter curve gives a bigger and more sudden jump in force and less time to react, so it demands more strength and skill.

Look again at the shortcut: felt weight = 1 + 2h ÷ r. The height is fixed by the ramp, so a smaller radius makes the number larger. In Teresa’s plans, both ramps are 1.2 meters tall. The 1.5 meter radius gives 1 + 2.4 ÷ 1.5 = 2.6 times body weight. The 2.5 meter radius gives 1 + 2.4 ÷ 2.5 = 1.96, about 2 times. The tight curve asks the legs to hold about 30 percent more force.

The force also arrives suddenly. On the flat bottom, a rider feels normal weight. The moment the wheels enter the curve, the felt weight jumps to its high value. Riders feel this as a jolt. Builders use the word for a harsh, sudden change in the surface itself, such as a bump or angle where the curve meets the flat, and a kink makes the jolt worse. A badly built ramp with a bump or flat spot where the curve meets the flat makes the kink worse. Smooth joints and a carefully drawn curve make the change feel gentler.

A tight curve also leaves less time. The rider covers the curve in a shorter distance, so there is less time to shift weight, bend the knees and stay square to the surface. Small errors grow fast. A mellow curve gives a learner more time to feel what is happening, which is why beginner ramps usually have wide transitions and low walls.

Tight curves are not wrong. Many experienced riders like them because they turn the board quickly and throw the rider up the wall. The point is fit. A ramp for a youth club with many beginners usually gets a wider radius. A ramp for advanced riders in a small space may use a tighter one.

Words to know
kink
a harsh, sudden change in a ramp's curve that riders feel as a jolt
mellow
skater word for a gentle, gradual curve or slope
felt weight
how heavy a rider feels, set by the normal force pushing up on them
Check yourself

1. Using felt weight = 1 + 2h ÷ r, what is the felt weight for h = 1.0 m and r = 2.0 m?

2. What is a kink on a ramp?

3. Why do beginner ramps usually have wide transitions?

Section 4

Building a Ramp

28.9

Ribs, Stringers and Plywood

Main ideaA wooden ramp is a frame of curved ribs joined by stringers and covered with layers of thin plywood bent to the curve.

Most wooden ramps share one structure. The sides are , flat pieces of thick plywood cut to the shape of the transition. Builders draw the curve on the first rib with a string and pencil, cut it, and trace it to make matching ribs. Ribs are spaced along the width of the ramp, with extra ribs for wider ramps, so the surface never spans a long gap.

Between the ribs run , pieces of framing lumber laid across the curve like rungs on a ladder. They sit close together, often every 20 to 30 centimeters, so the surface is supported at many points. Closer spacing is needed where the curve is steep and where riders land hardest, near the bottom.

The riding surface goes on in layers. Thin plywood bends to the curve without cracking, so builders screw down two or more thin layers, one over the other. They stagger the seams so the joints in one layer do not line up with the joints in the next. That keeps the surface from forming a ridge where sheets meet. A smooth top layer goes on last.

The coping is bolted along the top edge of the transition so it sits slightly proud, meaning it sticks out a little past the riding surface. The platform is framed like a small floor behind it. For an outdoor ramp, builders choose wood rated for weather, raise the frame off the ground and cover the ramp in rain, because wet plywood swells, warps and rots.

Words to know
ribs
flat pieces of plywood cut to the shape of the transition that form a ramp's sides and frame
stringers
framing pieces that run across between ribs to support the riding surface
stagger
to place joints so they do not line up from one layer to the next
Check yourself

1. What are the ribs of a ramp?

2. Why do builders stagger the seams in the surface layers?

3. Why are stringers placed closer together near the bottom of the curve?

28.10

Building Safely

Main ideaSafe ramp building means protecting the builders, choosing a good site and checking the finished ramp before every session.

Building a ramp uses saws, drills and heavy sheets of wood. Young builders work with an experienced adult who runs the power tools or watches closely. Everyone wears safety glasses, and hearing protection when saws run. Gloves help when carrying plywood, but builders keep loose gloves and sleeves away from spinning blades. Cords are kept out of walkways so no one trips.

Pick the site before buying wood. A ramp needs firm, level ground, with clear space around it and nothing hard nearby for a rider to hit. It should be away from streets, driveways and parked cars. Many towns have rules about structures in yards or shared spaces, so builders ask the property owner and check local rules first.

Details on the surface matter. Every screw head is driven slightly below the surface so wheels and knee pads do not catch on it. Sheet edges are sanded smooth. The coping is bolted tight, and its ends are capped or rounded. The first ramp a group builds should be small, because a low ramp is easier to learn on and a fall from it is shorter.

A finished ramp still needs care. Before each session, someone walks the surface looking for loose screws, cracked sheets, soft spots and gaps at the seams. Rain and sun wear plywood down, so the ramp is covered when not in use. A damaged section is fixed before anyone rides it again.

Words to know
safety glasses
protective eyewear worn when cutting, drilling or sanding
countersink
to drive a screw head slightly below the surface so nothing catches on it
inspection
a careful check of a ramp for damage before it is ridden
Check yourself

1. Why should every screw be countersunk?

2. Which is the best site for a backyard ramp?

3. What should happen before each riding session?

28.11

A Worked Design Problem

Main ideaGood ramp design puts the numbers together: height, radius, top angle, footprint, speed and felt weight, then checks them against the riders.

Return to the youth club. The lot is 9 meters long. The club wants a mini ramp 1.2 meters tall for mostly beginner and intermediate riders. Teresa proposes a 1.8 meter radius. The lot also needs room to walk around the ramp. Here is the full check, step by step, using the formulas from the earlier lessons.

First, the top angle. cos θ = 1 − 1.2 ÷ 1.8 = 0.333, so θ is about 70.5 degrees: steep but not vertical. Second, the footprint of each curve. Its length is 1.8 × sin 70.5° = 1.8 × 0.943 = 1.70 meters. Third, the speed at the bottom. v = √(2 × 9.8 × 1.2) = √23.52 = 4.85 meters per second, ignoring losses.

Fourth, the felt weight at the bottom: 1 + 2 × 1.2 ÷ 1.8 = 1 + 1.33 = 2.33 times body weight. That sits between the tight plan’s 2.6 and the wide plan’s 1.96. Fifth, the total length. Two curves at 1.70 meters each make 3.40 meters. A flat bottom of 2.4 meters brings it to 5.80 meters. Two platforms of 1.2 meters each add 2.40, for 8.20 meters. That fits the 9 meter lot with 0.80 meters to spare.

The design is not finished just because it fits. The club still checks the budget for plywood and lumber, plans staggered seams and close stringers at the bottom, and confirms a guardrail on each platform. If many riders are brand new, Teresa might also lower the ramp to 0.9 meters. Engineering is the habit of testing each choice against the people who will use it.

Words to know
design problem
a task with requirements and limits that is solved by planning, calculating and checking
mini ramp
a small halfpipe whose walls usually stop before vertical
halfpipe
a ramp with two facing transitions and usually a flat bottom between them
Check yourself

1. For h = 1.2 m and r = 1.8 m, what is the felt weight at the bottom?

2. The two curves are 1.70 m each, the flat bottom 2.4 m and each platform 1.2 m. What is the total length?

3. Why might the club lower the ramp to 0.9 meters?

Chapter review

Ramps by Design

0 / 8

1. What sets how tight or mellow a transition is?

2. A rider drops 2.0 m with no friction. What is the speed at the bottom?

3. Which energy change happens as a rider drops down a transition?

4. Where does a rider press up through the legs to pump?

5. After a 1.5 m drop on a curve with a 1.5 m radius, how heavy does a rider feel at the bottom?

6. What is the coping used for?

7. Why are thin layers of plywood used for the riding surface?

8. What does a drop-in setup look like?

Unit wrap-up

Engineering the Board and the Ramp

Twelve words, twelve meanings

0 / 12

Tap a word, then tap its meaning. A right pair locks in green.

Words
Meanings
Unit test

Fifteen questions across the unit

0 / 15

1. What is most often used to make a skateboard deck?

2. Why do some plies in a deck run across the board?

3. A deck is made 20 percent thicker. About how much stiffer does it get?

4. Which wheel is hardest?

5. Why does a soft wheel ride smoothly on rough ground?

6. What problem do riser pads help prevent?

7. What does a higher ABEC grade mean?

8. In a bearing, why does friction stay low?

9. A 54 mm wheel (circumference 0.170 m) rolls at 6.8 m/s. How many turns per second?

10. A curve has radius 3.0 m and the ramp is 1.5 m tall. What is cos θ at the top?

11. With no friction, what speed does a rider reach after a 0.9 m drop?

12. A 70 kg rider moves at 4 m/s at the bottom of a 2 m radius curve. What is the normal force?

13. Why does a tighter curve feel harder on the legs?

14. When a rider pumps, where do they press up through the legs?

15. Which step makes a ramp's surface safer for wheels and knee pads?

Spiral review

Five questions from earlier units

0 / 5

1. (Unit 13) Who founded Skateistan, and in what year?

2. (Unit 13) Why do skaters wax ledges?

3. (Unit 13) Metal knobs bolted along a granite ledge are an example of what?

4. (Unit 13) Which shows that skating contests are older than the Olympics?

5. (Unit 13) Which example of hostile design is aimed at people resting, not skaters?

Write it

Design a mini ramp for a group you know. Choose a height and a radius, then show each step of your arithmetic for the top angle, the curve's footprint, the speed at the bottom and the felt weight there. Explain one trade-off you made and why it fits your riders.

  • Use cos θ = 1 − h ÷ r for the top angle and r × sin θ for the footprint.
  • Use v = √(2gh) with g = 9.8 m/s² for the speed at the bottom.
  • Use 1 + 2h ÷ r for how many times their weight riders feel.
  • Say who the riders are and how your numbers suit them.
  • Name one safety step in building or checking the ramp.
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