## 20 Apr The physics of sports: Does a heavier bobsleigh make you go faster?

Now that athletes are reaching their physical peak, sports are turning to science to gain an advantage. Smoother swimsuits, lighter running shoes, more aerodynamic bicycles… there is even a maximum weight for bobsleighs! Let’s see what physics has to say about this, shall we?

## The forces on 2 bobsleighs with different masses

Let’s analyse the following example:

- Two bobsleighs,
**a**and**b,**are racing down an straight track. - mass of bobsleigh
**a**is bigger than the mass of bobsleigh**b**(**M**>_{a}**M**)._{b} - Other than their mass, the sleighs are identical.

Now check out the drawings beneath, about the force of gravity **F _{g}** on the 2 bobsleighs:

**F**_{g }=**Mg**, with**M**the mass of the sleigh and**g**the standard acceleration due to gravity.**F**_{g,}_{⊥}**= F**, the component of_{g}cos α**F**perpendicular to line of movement. (there is a geometric explanation for this)_{g}**F**, The component of_{g,// }= F_{g}sin α**F**parallel to line of movement._{g}**F**_{n}**= F**_{g,}, the normal force._{⊥}**F**=_{f }**μ**, the force of friction (dry friction), with_{k}F_{n}**μ**the kinetic coefficient of friction for given surfaces._{k}**F**sum of all the forces, the resulting force._{res}=

## Different mass, same acceleration

The formulas above show you that if, for example, bobsleigh **a** is 2 times heavier than bobsleigh **b**, the resultant force on bobsleigh **a **is also 2 times bigger than the force on **b **(check for yourself, if you want to!), and with Newton’s second law of motion, you have:

**F**_{res,a}= 2F_{res,b}**M**_{a}= 2M_{b}**F**, with_{res}= Ma →*a*= F_{res}/Mthe acceleration.*a*

So you get exactly the same acceleration (and in equal begin circumstances: velocity) for both bobsleighs. Yet no advantage for the heavier sleigh **a**

## But what about the air resistance?

In the calculations above we considered only the forces dependent on gravity. But there is an extra force present: air resistance,

**F _{a} = ½pv^{2}CA**

with

**the air density,**

*p***v**the sleighs velocity,

**C**a given coefficient and

**A**the frontal area of the sleigh. There is no mass in this formula, so if both sleighs have the same speed, the air resistance will be the same for both (see the drawings below).

If you take air resistance into account, you have to substract it _{ }from the considered **F _{res}** . And because the air resistance is the same for both sleigh, you need to take a bigger percentage from

**F**than from

_{res,b}**F**.

_{res,a}So with the example that **M _{a } = 2M_{b}** and

**v**is the same, you get:

- For bobsleigh
**a**:**F**_{res,a,new }= F_{res,a,old}– F_{a }= 2F_{res,b,old}– F

And *a*** = F/M = (2F _{res,b,old} – F_{a})/2M_{b} = F_{res,b,old}/M_{b} – F_{a}/2M_{b}.**

- For bobsleigh
**b**: F_{res,b,new}**= F**_{res,b,old}– F_{a .}

And *a ***= F/M = (F _{res,b,old} – F_{a})/M_{b} = F_{res,b,old}/M_{b} – F_{a}/M_{b.}**

So the effect of air resistance on acceleration is 2 times smaller with the heavier sleigh **a**. Therefore the heavier sleigh **a** will accelerate more and will become faster than sleigh **b**.

## Possible negative effects of heavier bobsleighs

This bobsleigh example gives you a physical basis that heavier sleighs go faster. But if the pilot can’t steer properly because of the bigger mass, or if the pusher isn’t strong enough to accelerate much, the loss will be bigger than the gain.

So what do you think about this? Should sports turn to science for better equipment, to amp up results where human ability can’t anymore, or is it comparable with doping/cheating and should it all be about the athletes’ skills? Let’s discuss it in the comment section!

WTFsimon

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