# Commuting - Does weight affect downhill speed?

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imi
06-27-09, 01:51 AM
I've seen a number of posters mention that they are faster downhill (coasting) because of their heaviness.

Gravity is the same for any mass falling in a vacuum (right?), but there are many other factors and more physics going on in a downhill bike coast than gravity in a vacuum... acceleration, momentum, air resistance, road friction, etc...

Anyone with the physics knowledge can sort this one out? Basically two riders on exactly the same rigs, all conditions being equal coasting down a hill, the only difference being that one weighs twice as much as the other with comparable extra girth.

Starting from zero mph who will get off to the best start? Will the other one catch up or overtake somewhere down the hill? Who will get further up the next hill by just coasting?

cheers!

Andy_K
06-27-09, 02:14 AM
Assuming similar aerodynamics (a bad assumption, but go with it for a second), a heavier rider will have an easier time overcoming air resistance because he will have greater momentum. Think of dropping a baseball vs. dropping a wiffle ball. So that's what gives the heavier rider an advantage.

Of course, a heavier rider is likely to present a larger cross-section than a lighter rider, so some of this advantage will be lost but not all. Put the heavier rider on a recumbent and it's no contest, even with the extra air resistance from his beard.

imi
06-27-09, 02:25 AM
uh, assuming same cross section the wiffle ball and the baseball would fall at the same rate, and hit the ground simultaneously if dropped from a high building. From Wiki:

"In physics, gravitational acceleration is the acceleration of an object caused by the force of gravity from another object. In the absence of any other forces, any object will accelerate in a gravitational field at the same rate, regardless of the mass of the object. On the surface of the Earth, all objects fall with an acceleration of somewhere between 9.78 and 9.82 m/s"

Andy_K
06-27-09, 02:28 AM
uh, assuming same cross section the wiffle ball and the baseball would fall at the same rate, and hit the ground simultaneously if dropped from a high building. From Wiki:

"In physics, gravitational acceleration is the acceleration of an object caused by the force of gravity from another object. In the absence of any other forces, any object will accelerate in a gravitational field at the same rate, regardless of the mass of the object. On the surface of the Earth, all objects fall with an acceleration of somewhere between 9.78 and 9.82 m/s"

Note the bold part here. Try it. Wiffle balls aren't very good at overcoming air resistance.

imi
06-27-09, 02:41 AM
ah right! thanks Andy K. :) in a vacuum this would be true... so we have the heavier dude having an advantage due to his mass, and the lighter guy having an advantage as he is more aerodynamic (right?)... please note I started this post due to my ignorance of the physics involved, not trying to prove a personal assumption :)

The heavier guy would cause the tires to have a wider contact with the road thus increasing friction and slowing him down (right?)

Andy_K
06-27-09, 02:56 AM
I think that's right.

If both riders are coasting (assumptions like this make physics much easier), the forces acting on them will be gravity pushing them down (which is proportional to their mass) and air resistance pushing them back (which is independent of their mass but increases with velocity). At some point, the force from air resistance will equal the force from gravity, and the rider will no longer accelerate without pedaling (terminal velocity). The heavier rider will require a greater force from air resistance to reach terminal velocity, which means if they had similar aerodynamics, he'd be going faster when he reached terminal velocity.

I think the difference in aerodynamics is less significant. It's also more complicated. The heavier rider, while having a larger cross section, may also be more round/less flat. I'm not sure how it would work out.

trekker pete
06-27-09, 07:23 AM
Assuming a good wheelset and properly inflated tires, I believe the rolling resistance differences are negligible.

Weight is a different story. Twice the weight means twice the force.

Aerodynamics I think are a bit of a factor, but, I don't think they come close to the weight factor.

So, yes, fat dude will pwn skinny guy on the downhills, assuming he is a fit fat dude.

Of course, he will give it back, plus interest when it's time to climb, so, you ain't gonna see many XXL yellow jerseys.

trekker pete
06-27-09, 07:25 AM
The heavier rider, while having a larger cross section, may also be more round/less flat. I'm not sure how it would work out.

It's called the aerobelly. Comes with the beard and technical degree as standard equipment on a recumbent.

Fremdchen
06-27-09, 07:36 AM
so, you ain't gonna see many XXL yellow jerseys.

Except on ebay, were I got mine! :-)

Jtgyk
06-27-09, 10:37 AM
All I know is that at 360lbs I manage to coast downhill faster than some people pedaling downhill.
(This drives my buddy nuts....of course , he kick my butt when it coms to climbing)

djwid
06-27-09, 10:59 AM
It's called the aerobelly. Comes with the beard and technical degree as standard equipment on a recumbent.
Sure it does
http://www.raceacrossamerica.org/blog/blogs/media/blogs/RAAM4p/TeamRans2.jpg
http://farm4.static.flickr.com/3643/3558054907_30832f7e88.jpg

...

ellerbro
06-27-09, 11:48 AM
Anyone care to do an experiment to test it out? Get two people of significantly different weights. Have them go from a stop down a slight decline so they don't get going too fast, on the same bike of course. This should eliminate wind resistance from the equation. Use a stopwatch and time them from A to B. Try it again down a steep hill where wind resistance will have more of an effect.

Your results will be an important contribution to the world cycling community.

JTGraphics
06-27-09, 11:51 AM
I can tell you that my friend and I have done this test several times and it always comes out the same. I weight 163 lbs. and he is 115 lbs.
We climb up this hill all the time and come back down its about 1.5 mile downhill all the way down with a grade range of 3 – 10% without pedaling we start out at about 15 mph and coast all the way and I’ll hit 39 – 40 mph he gets up to about 37 – 38 mph and I’ll get to the bottom about 5 – 10 seconds before him.
He says that as soon as we start I’m pulling away and he never gains any distance the entire way down I just leave him.
Why who knows you tell me but the results are always the same.

supramax
06-27-09, 12:15 PM
If you drop a 10 pound rock and a 100 pound rock from the same height at the same time; they both reach the ground at the same time.

That being said, my fastest speed on a bike (58 miles an hour) was reached going downhill on a fully loaded bike (front and rear panniers and handlebar bag, sleeping bag and pad and tent. The load was approximately 85 pounds. If you're adept at riding with load, the bike is a tremendously stable (downhill) rocket.

cooker
06-27-09, 12:24 PM
If you drop a 10 pound rock and a 100 pound rock from the same height at the same time; they both reach the ground at the same time.
That actually isn't completely true. If you dropped them from a plane at high altitude, the heavier rock, if it was made of the same material, and shaped about the same, would hit sooner as it would reach a higher terminal velocity. If it was made of lighter material, like limestone compared to marble, it might hit later. If it was sculpted into a wide sheet with a slight bowl shape, it might drift off target or shimmy down like a sheet of paper. If one rock was shaped like a spear it would drop faster than one shaped like a snowflake.

If you dropped them from 20 feet, they'd hit pretty much at the same time.

Febs
06-27-09, 12:26 PM
If you drop a 10 pound rock and a 100 pound rock from the same height at the same time; they both reach the ground at the same time.

In a vacuum, yes. In an atmosphere, not necessarily.

supramax
06-27-09, 12:30 PM
Does the name 'Galileo' ring a bell? :)

cooker
06-27-09, 12:35 PM
Basically, the gravitational force is proportional to the weight of the rider while air resistance is proportional to cross sectional area. A rider who is twice as heavy as another rider - say 220 lbs vs 110 lbs, is not usually anywhere near twice as big in cross section. Weight increases roughly in proportion to the cube of height or waist circumferance, while cross section increases roughly in proportion to the square of height or waist circumferance. So in downhill coasting, weight pwns aerodynamics.

hairnet
06-27-09, 12:45 PM
Just from personal observation, yes. I've gone down some long steep hills with people 20,30,30,50 pounds lighter than me and I've gone at their speed, or go faster than them, just coasting as they pedal.

I guess I should add that I'm 200 pounds and rather lean/skinny.

Shimagnolo
06-27-09, 12:45 PM
Ride around the hills and mountains of CO, and you will see examples every day;
On the climbs, it is the little people who leave the big people (like myself) behind.
Then on the descents, the little people get left behind.

As for dropping two objects of different weights;
Ask any skydiver if a heavy person and a light person fall at the same rate.
As someone else pointed out, that is true only in a vacuum.
Small skydivers on freefall teams routinely wear lead weights to bring their fall rates up to the same as their bigger teammates.

supramax
06-27-09, 12:49 PM
Get this through your heads, guys: The speed of a falling body is independent of its weight. This is a scientific fact, a law.

Febs
06-27-09, 12:57 PM
Get this through your heads, guys: The speed of a falling body is independent of its weight. This is a scientific fact, a law.

OK, Galileo. :rolleyes:

I just dropped a book and a single sheet of paper from the same height. The book hit the ground first. Someone call the physics police! I broke the scientific law according to supramax!

In all seriousness, you need to understand that air resistance imparts a force on a falling object and that your "scientific fact" is only true of an object in a vacuum. Put a 1 lb weight on a small parachute. Put a 1 ton weight on the same parachute. Do you think that they'll fall at the same rate?

Shimagnolo
06-27-09, 12:58 PM
Get this through your heads, guys: The speed of a falling body is independent of its weight. This is a scientific fact, a law.

Vt = sqrt((2 * m * g) / (rho * A * Cd))

where

Vt = terminal velocity,
m = mass of the falling object,
g = acceleration due to gravity,
Cd = drag coefficient,
rho = density of the fluid through which the object is falling, and
A = projected area of the object.

Do you see that term "m * g"?
That is called w_e_i_g_h_t.

pacificaslim
06-27-09, 01:05 PM
Get this through your heads, guys: The speed of a falling body is independent of its weight. This is a scientific fact, a law.

A law that only applies "in a vacuum".

JanMM
06-27-09, 01:13 PM
Observational data: I routinely pass single upright bikes going downhill, both on a tandem with my wife/stoker, and on my recumbent. I weigh a bit less than 200#. Stoker weighs a lot less. The bikes are a bit heavier than average. Moderate cross-section tires running at about 90-95psi on both bikes.

The speeds are directly affected by my/our energy input and by physical forces beyond our control.

supramax
06-27-09, 01:14 PM
OK, Galileo. :rolleyes:

I just dropped a book and a single sheet of paper from the same height.
The book hit the ground first. Someone call the physics police!
I broke the scientific law according to supramax!

In all seriousness, you need to understand that air resistance imparts a force on
a falling object and that your "scientific fact" is only true of an object in a vacuum.
Put a 1 lb weight on a small parachute. Put a 1 ton weight on the same parachute.
Do you think that they'll fall at the same rate?

Most people use feathers for that experiment. :p
To repeat: "The speed of a falling body is independent of its weight."

cooker
06-27-09, 01:25 PM
To repeat: "The speed of a falling body is independent of its weight."
It's a meaningless statement.

rm -rf
06-27-09, 01:31 PM
Basically, the gravitational force is proportional to the weight of the rider while air resistance is proportional to cross sectional area. A rider who is twice as heavy as another rider - say 220 lbs vs 110 lbs, is not usually anywhere near twice as big in cross section. Weight increases roughly in proportion to the cube of height or waist circumferance, while cross section increases roughly in proportion to the square of height or waist circumferance. So in downhill coasting, weight pwns aerodynamics.

This is why heavier riders are faster on downhills. And it's the same reason that sprinters can be big and strong. Their extra power for a slightly larger aerodynamic resistance makes them faster in a sprint than lightweight riders.

Sixty Fiver
06-27-09, 01:46 PM
My friend weighs 100 pounds more than I do and I own his ass on climbs, we're pretty even on the flats, but on down hills I have to pedal like a gerbil on crack just to hold his back wheel.

On my own I have noticed that my bikes that are heavier descend faster when they are coasting... when I was a kid we used to make pinewood cars and after making them as aero as possible the best way to make them go faster was to add weight that exceeded the enforced limits.

I do not ride in a vacuum... the spacesuit kills my aerodynamics.

Andy_K
06-27-09, 01:50 PM
To repeat: "The speed of a falling body is independent of its weight."

I would think that anyone who has ridden a bike would understand that bicyclists start to react more like a feather than like a lead weight when traveling above 15 mph.

xenologer
06-27-09, 01:58 PM
Assuming a good wheelset and properly inflated tires, I believe the rolling resistance differences are negligible.

Weight is a different story. Twice the weight means twice the force.

Aerodynamics I think are a bit of a factor, but, I don't think they come close to the weight factor.

So, yes, fat dude will pwn skinny guy on the downhills, assuming he is a fit fat dude.

Of course, he will give it back, plus interest when it's time to climb, so, you ain't gonna see many XXL yellow jerseys.

However, does twice the force equate to twice as fast down the hill?
Regardless of somethings weight, his Acceleration is what is important for the downhill race.
Force=Mass*Acceleration
Acceleration=Force/Mass
In other words, while the guy twice as big recieves twice as much force from gravity, he also has twice as much mass which cancels out the benefit.

Andy_K
06-27-09, 02:12 PM
In other words, while the guy twice as big recieves twice as much force from gravity, he also has twice as much mass which cancels out the benefit.

This is true, but you have to consider all the forces acting on the rider. The net force is the gravitational force minus the force of air resistance. Air resistance increases as speed increase. At some point, the gravitational force is canceled out by the force of air resistance, at which point the rider will cease to accelerate and maintain a constant speed (assuming incline, wind, etc. remain constant). This is called terminal velocity. A heavier rider has a higher terminal velocity.

supramax
06-27-09, 02:14 PM
I would think that anyone who has ridden a bike would understand that bicyclists start to react more like a feather than like a lead weight when traveling above 15 mph.

Goddamn air resistance! :(

supramax
06-27-09, 02:28 PM
RE: "The speed of a falling body is independent of its weight."

It's a meaningless statement.

It's considered to be the discovery of a genius, brainiac! :p

JTGraphics
06-27-09, 02:29 PM
This is true, but you have to consider all the forces acting on the rider. The net force is the gravitational force minus the force of air resistance. Air resistance increases as speed increase. At some point, the gravitational force is canceled out by the force of air resistance, at which point the rider will cease to accelerate and maintain a constant speed (assuming incline, wind, etc. remain constant). This is called terminal velocity. A heavier rider has a higher terminal velocity.

As shown in my previous post I will always hit my top speed and that’s it, this is with no more than a 2 mph head wind more and its slower. My friend also only hits his top speed no more at the same head wind.
Sure drag differences are in effect here, I am really getting aero on these downhill tests we do, when I sit up at the bottom to slow speed drops quite fast to low 30's till we need to turn and apply brakes.

ellerbro
06-27-09, 02:30 PM
So what about at slow speeds where air resistance is negligible? Does the heavy rider accelerate faster from the very beginning or does the advantage only begin once the lighter rider has reached terminal velocity?

JTGraphics
06-27-09, 02:34 PM
As I also posted in my previous post I'm not looking back at him but he tells me from the start I start to gain distance on him and as we increase speed that gap gets bigger.
This is fact, as we do these downhill runs and its always the same.

06-27-09, 04:03 PM
I think we need more 'bent riders in here, for they have aerobellies, beards and degrees in physics.

JanMM
06-27-09, 04:09 PM
I think we need more 'bent riders in here, for they have aerobellies, beards and degrees in physics.

Sorry, no degree in Physics but I am subject to the Laws of Physics.

http://i189.photobucket.com/albums/z284/JanMM/jmvrex3.jpg

supramax
06-27-09, 04:40 PM
Sorry, no degree in Physics but I am subject to the Laws of Physics.

http://i189.photobucket.com/albums/z284/JanMM/jmvrex3.jpg

What a drag! :)

ellerbro
06-27-09, 07:13 PM
I posted the question over on physicsforums.com and the three responses I've gotten are that a heavy and light cyclist will have the same acceleration (a = g*sin(theta)), and therefore speed, when coasting down a hill. That is, until wind resistance comes into play.

swwhite
06-27-09, 07:32 PM
Vt = sqrt((2 * m * g) / (rho * A * Cd))

where

Vt = terminal velocity,
m = mass of the falling object,
g = acceleration due to gravity,
Cd = drag coefficient,
rho = density of the fluid through which the object is falling, and
A = projected area of the object.

Do you see that term "m * g"?
That is called w_e_i_g_h_t.

Plus, with the coefficient of drag in the denominator, a higher number gives a lower velocity. (I suppose; I wasn't very good in physics).

trekker pete
06-27-09, 07:40 PM
However, does twice the force equate to twice as fast down the hill?

no, drag increases at, uhhh, I think it's the square of speed.

Regardless of somethings weight, his Acceleration is what is important for the downhill race.

depends on the length of the race

Force=Mass*Acceleration
Acceleration=Force/Mass
In other words, while the guy twice as big recieves twice as much force from gravity, he also has twice as much mass which cancels out the benefit.

Not sure about the math on that part. What I am sure about was on my ride today I met up with a guy. We rode for about 15 miles together, mostly level, some short hills. We seemed a pretty good match on level ground, but on descents I ran away from him pretty badly. He said I was pretty nasty going down those hills. My response was that at least those extra 50 lbs I drag around are good for something. I am guessing I had about 30 lbs on him.

To supramax's statements concerning dropping stuff and galileo, similar shaped object weighing something close resonably close to each other will drop at approximately the same speed over a relatively short distance. The same object dropped from higher distances will certainly NOT drop at the same speed. Given similar aerodynamics, the lighter object will reach terminal velocity at a lower speed. It's not even open to debate. It is a fact. More weight=more force. More force=higher terminal velocity

Andy_K
06-27-09, 07:42 PM
I posted the question over on physicsforums.com and the three responses I've gotten are that a heavy and light cyclist will have the same acceleration (a = g*sin(theta)), and therefore speed, when coasting down a hill. That is, until wind resistance comes into play.

Well, that's not very helpful. How fast do you need to be going before wind resistance comes into play? It's always in play, but becomes a big factor at about 15 mph.

Now it happens that while I don't ride a recumbent, I do have both an aerobelly and a degree in physics. I haven't used the physics degree lately and I'm lazy (which is why I haven't thought this through with any kind of rigor up to now), but this is the way I see it:

Let's say rider A weighs 220 and rider B weighs 110. The force due to gravity will vary depending on the slope, but it came be simplified as

F(g)(a) = 2x
F(g)(b) = x

where x is the weight of rider B times a factor to account for the incline. Now lets call the force from wind resistance y. For any given speed it will be about the same for both riders. So the net forces will be

F(net)(a) = 2x - y
F(net)(b) = x - y

Now for simplicity, let's consider the case where the gravitational force in for rider B is twice the force from wind resistance (x = 2y).

F(net)(a) = 4y - y = 3y
F(net)(b) = 2y - y = y

So at that speed (below terminal velocity), the rider with twice the weight will be experiencing three times the force, and therefore will be experiencing greater acceleration, even after you account for his greater weight.

All of the above is completely off the cuff. I may have made some really gross errors. Does it make sense to anyone else?

trekker pete
06-27-09, 07:46 PM
I posted the question over on physicsforums.com and the three responses I've gotten are that a heavy and light cyclist will have the same acceleration (a = g*sin(theta)), and therefore speed, when coasting down a hill. That is, until wind resistance comes into play.

And wind resistance comes into play pretty quickly. Cyclists, particularly upright cyclists are absolutely horrible at being aerodynamic.

Anybody know the average Cd of a typical roadie in the drops? I suspect it is marginally better than a parachute. Hell, maybe the chutes better. It just has a lot more cross section.

trekker pete
06-27-09, 07:53 PM
Now it happens that while I don't ride a recumbent, I do have both an aerobelly and a degree in physics. I haven't used the physics degree lately and I'm lazy (which is why I haven't thought this through with any kind of rigor up to now), but this is the way I see it:

The laziness probably explains the aerobelly. :)

How 'bout a beard?

I got about 6 years left in the navy reserve and by my calculations, I figure my lower backs got about that much time left as well. So, in 6 years I'm pretty sure I'll be on a bent since the back will be done, I won't have grooming standards to follow and I'm certain my aerobelly will still be around. If I start hitting night classes now, maybe I can have the tech degree too.

Andy_K
06-27-09, 07:56 PM
How 'bout a beard?

Only in the winter. :)

Shimagnolo
06-27-09, 07:56 PM
no, drag increases at, uhhh, I think it's the square of speed.

Correct. The acceleration is the derivative of the formula I gave earlier:

acceleration = g - ((Cd * rho * V^2 * A) / (2 * m))

where

V = *current* velocity,
m = mass of the falling object,
g = acceleration due to gravity,
Cd = drag coefficient,
rho = density of the fluid through which the object is falling, and
A = projected area of the object.

And for a vehicle coasting down a descent (ignoring friction of bearings and tires):

acceleration = (sin(theta) * g) - ((Cd * rho * v^2 * A) / (2 * m))

where theta is the angle, (measured as zero for a level surface)

supramax
06-27-09, 08:11 PM
To supramax's statements concerning dropping stuff and galileo, similar shaped object weighing something close resonably close to each other will drop at approximately the same speed over a relatively short distance. The same object dropped from higher distances will certainly NOT drop at the same speed. Given similar aerodynamics, the lighter object will reach terminal velocity at a lower speed. It's not even open to debate. It is a fact. More weight=more force. More force=higher terminal velocity

I don't know what you mean by the word 'fact', but you're incorrect. A 50 lb dumbbell dropped at the same time and from the same height as a penny, will reach the ground the same time the penny does.

TwoShort
06-27-09, 08:13 PM
RE: "The speed of a falling body is independent of its weight."

False.

It's considered to be the discovery of a genius, brainiac! :p

No, it's very similar to a discovery by a genius, but actually, heavier things fall faster. Except in a vacuum, which isn't relevant because we don't ride bikes there. The whole Gallileo-Tower-of-Pisa legend is a nice story, but it never happened. Not only because there is no actual record of it, but because it would not have worked. Drop two balls of identical cross section and differenct mass, and the heavy one will hit the ground first. It took a genius (Gallileo) to figure out that acceleration due to gravity was the same for both balls anyway. Gravity pulls harder on the heavier ball (or cyclist) but the greater inertia balances that out. Air resistance (at a given speed) pushes equally on both balls (or cyclists) but the greater momentum of the heavier one overpowers it more.

Hence, after my much more hard core buddy drags my sorry butt up a mountain, I can coast down next to him while he cranks like crazy just to keep up.