Video: Crazy three-wheel downhill racing from Kentucky - lots of fun!

KnowThyInnerTube wrote:

...and my point would be that at the top of the hill, the trike and rider have potential energy equal to E=mgh (combined mass x gravitational field strength x height of the hill) and this energy is converted to kinetic (movement energy) of the form E = half m vsquared (sorry I'm too lazy to find half and squared) All of the potential energy gets converted to kinetic energy (less frictional losses) therefore mgh=half mvsquared. Rearranging for v gives us v= square root 2gh. i.e. the final speed (elocity is independent of mass because it cancels out.

The trick is with the frictional losses which you haven't included in the equation. On a bike, the main frictional losses are rolling resistance and air resistance. Both of those aren't related to mass and would be approximately equal at the same speed for light and heavy riders (the heavy ones might be a bit less aerodynamic) and would appear as a constant:

mgh - friction = ½mv².

thus,

v = √2(gh - friction/m)

and you'd get a weight advantage going downhill (not so much uphill). It's a more noticeable effect on an incline as your terminal velocity is a lot less than freefalling - that's why the bottle experiment would require very accurate equipment to spot the difference.

I'm not a physics teacher, so here's NASA's explanation of terminal velocity:

https://www.grc.nasa.gov/www/k-12/airplane/termv.html

and in red, it states "Objects do not fall at the same rate through the atmosphere"

ianrparsons wrote:

AAAARGH! I teach Physics. The laws are simple to state and difficult to understand, hence the confusion shown in the above discusions, including some suspect maths!

Gravity creates weight, measured in Newtons; from mass, measured in Kilograms. The acceleration due to gravity is constant, in round figures 10 meters per second per second on the Earth. Easy practical check to do. Take two identical 500ml plastic bottles e.g Coke. Fill one with water the other leave empty. Hold them by the neck and drop them simultaneously, they land together, equally accelerated by Gravity even though their masses and therefore their weights are different. The air resistance that opposes movement is equal because the bottles are identical in shape, could put a little water in the empty one to ensure it stays upright. It works!

Check out Apollo 17 mission videos where a hammer and feather are dropped simultaneously on the moon, they land together. It is on You Tube.

To check this out for cyclists going down hill you will need two IDENTICAL cycles, with very different sized riders. The lighter rider should have less friction and go a little quicker. Difficult to control all the possible variables to get reproduceable results. It can be done with school lab stuff using ramps, trolleys and electronic data loggers that can measure speed and acceleration quite precisely.

I weigh 20 stone. My 10 and 12 stone riding companions just cannot keep up, whatever bike, whatever clothing, whatever luggage, when we're freewheeling downhill.  They often can't keep up pedalling flat out while I'm freewheeling.  The heavier you are, the faster you go downhill. I can't do the maths, but I know the effect is real.

Deltavelo wrote:

If what you say were true Bez, then for example two steel balls of equal diameter but one solid and the other hollow would fall at different rates. This is not so, they fall at the same rate both in a vacuum and in the air.

Nope, in air the solid ball will fall quicker, the only question is whether it is a noticable amount or a tiny fraction of a percent.

As a thought exercise, take it to the extreme.  The hollow ball is made of steel so thin that it is as light as foil, the solid ball weighs as much as a bowling ball.  The difference then should be obvious, and what becomes apparent then will remain true even if the hollow ball becomes heavier.

bikebot wrote:

Deltavelo wrote:

If what you say were true Bez, then for example two steel balls of equal diameter but one solid and the other hollow would fall at different rates. This is not so, they fall at the same rate both in a vacuum and in the air.

Nope, in air the solid ball will fall quicker, the only question is whether it is a noticable amount or a tiny fraction of a percent.

As a thought exercise, take it to the extreme.  The hollow ball is made of steel so thin that it is as light as foil, the solid ball weighs as much as a bowling ball.  The difference then should be obvious, and what becomes apparent then will remain true even if the hollow ball becomes heavier.

 

 

 

If both balls weigh the same, think how large the hollow ball would need to be compared with the solid one and then ask yourself if it would still fall slower.

Beatnik69 wrote:

bikebot wrote:

Deltavelo wrote:

If what you say were true Bez, then for example two steel balls of equal diameter but one solid and the other hollow would fall at different rates. This is not so, they fall at the same rate both in a vacuum and in the air.

Nope, in air the solid ball will fall quicker, the only question is whether it is a noticable amount or a tiny fraction of a percent.

As a thought exercise, take it to the extreme.  The hollow ball is made of steel so thin that it is as light as foil, the solid ball weighs as much as a bowling ball.  The difference then should be obvious, and what becomes apparent then will remain true even if the hollow ball becomes heavier.

 

 

 

If both balls weigh the same, think how large the hollow ball would need to be compared with the solid one and then ask yourself if it would still fall slower.

Of course it would fall slower it would weigh the same as the other ball, but would be the size of a house and so would have to displace a lot more air to move.

An easy test would be to get two balloons, inflate one and then drop both, the inflated one will fall slower, even though it weighs slightly more now (assume air inside the balloon is at a greater pressure than atmospheric pressure and that inflating also included some mositure content.) it definitley does not weigh less

Acceleration due to gravity is a function of mass, deceleration due to bearing and tyre friction is also a function of weight, but deceleration due to wind resistance is a function of surface area and shape and surface roughness, but unrelated to mass.

Beatnik69 wrote:

bikebot wrote:

Deltavelo wrote:

If what you say were true Bez, then for example two steel balls of equal diameter but one solid and the other hollow would fall at different rates. This is not so, they fall at the same rate both in a vacuum and in the air.

Nope, in air the solid ball will fall quicker, the only question is whether it is a noticable amount or a tiny fraction of a percent.

As a thought exercise, take it to the extreme.  The hollow ball is made of steel so thin that it is as light as foil, the solid ball weighs as much as a bowling ball.  The difference then should be obvious, and what becomes apparent then will remain true even if the hollow ball becomes heavier.

If both balls weigh the same, think how large the hollow ball would need to be compared with the solid one and then ask yourself if it would still fall slower.

That isn't what was proposed "two steel balls of equal diameter".  However, in your example, yes the larger hollow ball of equal mass would fall slower.  If I remember correctly, the drag coefficient of a sphere simply increases as the square of the radius.

Deltavelo wrote:

If what you say were true Bez, then for example two steel balls of equal diameter but one solid and the other hollow would fall at different rates. This is not so, they fall at the same rate both in a vacuum and in the air.

No, they don't. Let's say your hollow ball has mass M and the solid ball has mass 2M. When you release them, the gravitational (downward) forces acting on them are gM and 2gM respectively. Obviously, dividing the foce by the mass gives acceleration, which is g in both cases.

Let's brush over differential calculus for now and assume they accelerate at the same rate until they reach a certain velocity V. The downward forces on each remain the same, obviously: gM and 2GM respectively. But they both have a drag force which acts upwards and which is dependent only on their body profile and their velocity, not their mass. So both balls experience an upward force F.

Now your hollow ball has a net downward force of gM-F and your solid ball has a net downward force of 2gM-F.

To work out their acceleration, you need to divide force by mass in each case, giving you g-F/M for the hollow ball and g-F/2M for the solid ball.

Clearly, F/M > F/2M, therefore the solid ball accelerates more quickly for a velocity V. And notice that there is no constraint on V: the only time they both experience the same acceleration is the instant you release them. Once they are freefalling, the solid ball is always accelerating at a greater rate. (Until both have reached their terminal velocities, when the solid ball will be moving faster.)

Deltavelo wrote:

Here is a thought experiment: imagine freewheeling down hill with a buddy and you link arms, do you suddenly start accelerating because you now weigh twice as much? I think not.

So my original point stands, aerodynamics, friction and pedalling/braking  are the only factors, not the weight of the extra body.

Your thought experiment is not relevant because neither your mass nor your air resistance changes. Put you and your friend on a tandem, (reduce air resistance compared to riding side by side) and I promise you you'll go down the hill faster.

The error in your reasoning is explained here: http://physics.stackexchange.com/questions/75942/terminal-velocity-of-tw...

The relevance of this to cyclists is evident when you ride down a hill with a heavier rider. The heavier ride will be significantly faster down the hill than the lighter rider. I think this was also what started the discussion.

If you want a relevant thought experiment, that would be to have two parachutists at terminal velocity. One is weighs twice as much as the other. The heavier one descends faster.

It is really the same as the sheet of paper and the sheet of lead. Same shape, same aerodynamic drag, fall at very different speeds.

Terminal velocity on a bike is the speed you reach down a hill without pedalling or braking. It's not that high on a moderate gradient.

Deltavelo wrote:

So, what exactly is a "weight advantage" when falling solely due to gravity? I seem to remember that a chap named Galileo back in the 16th century demonstrated that gravity acts on all falling bodies independently of their mass. So why is it that so many people get this wrong? On an inclined plane (hill), factors affecting speed are friction and aerodynamics, but not weight! Please don't persist with this erronious idea.

Oh, and it seems that they get going by pedalling and have brakes and/or feet on the ground, just might have something to do with differing speeds.

Apart from that, this looks like a hoot!

You can get a weight advantage if the friction is significant in slowing the vehicles down but I'd be surprised if these trikes have high enough friction to make it worthwhile.

Deltavelo wrote:

So why is it that so many people get this wrong? On an inclined plane (hill), factors affecting speed are friction and aerodynamics, but not weight! Please don't persist with this erronious idea.

Because the increased weight means wind resistance has less of an effect. Drop a sheet of paper, and a sheet of lead, the lead will hit the floor first unless there are some unusual factors at play. In a vacuum they'll hit at the same time.

These people aren't in a vacuum so I'm not sure what you're stating is erronious.

danthomascyclist wrote:

These people aren't in a vacuum

They're in Kentucky so a lot of people would disagree.

Deltavelo wrote:

I seem to remember that a chap named Galileo back in the 16th century demonstrated that gravity acts on all falling bodies independently of their mass. So why is it that so many people get this wrong? On an inclined plane (hill), factors affecting speed are friction and aerodynamics, but not weight! Please don't persist with this erronious idea

As above, unfortunately it's your idea that's erroneous

Gravitational force is proportional to weight, but aerodynamic drag is independent of weight.

If you double the weight of the vehicle by welding one to the side of the other, so the two occupants are sitting side by side, the gravitational force will double and the aerodynamic drag will also (roughly) double, so you'll gain no advantage: the acceleration will be broadly the same.

If you (nearly) double the weight by sitting one person behind the first, you'll (nearly) double the gravitational foce but you'll have only a modest effect on the aerodynamic drag. Result: a greater ratio of forcepulling the vehicle forwards on the slope to mass of the vehicle, ie greater acceleration, and a higher terminal velocity.