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

Dutch Women in bobsleigh riding through a curve during the final of the 2010 Olympic winter games in VancouverDutch women bobsleigh in the final of the 2010 Olympic Games. Image: Duncan Rawlinson

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 (a > Mb).
  • Other than their mass, the sleighs are identical.

Now check out the drawings beneath, about the force of gravity g on the 2 bobsleighs:

  • Fg = Mg , with M the mass of the sleigh and g the standard acceleration due to gravity.
  • Fg, = Fg cos α , the component of Fg perpendicular to line of movement. (there is a geometric explanation for this)
  • Fg,// = Fg sin α , The component of g parallel to line of movement.
  • Fn = Fg, , the normal force.
  • Ff = μkFn , the force of friction (dry friction), with μk the kinetic coefficient of friction for given surfaces.
  • Fres­= sum of all the forces, the resulting force.
beeld_Mb1_Simon Grannetia

sleigh a racing down the sraight track with al the forces sketched. Image: Simon Grannetia

beeld_Ma1_Simon Grannetia

sleigh b racing down the sraight track with al the forces sketched. Image: Simon Grannetia

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:

  • Fres,a = 2Fres,b
  • Ma = 2Mb
  • Fres = Ma → a = Fres/M, with a the acceleration.

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,
Fa = ½pv2CA
with p the air density, 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).

sleigh a racing down the sraight track with al the forces sketched.

sleigh a racing down the sraight track with al the forces sketched, inlcuding friction
Image: Simon Grannetia

sleigh b racing down the sraight track with al the forces sketched.

sleigh b racing down the sraight track with al the forces sketched, inlcuding friction
Image: Simon Grannetia

If you take air resistance into account, you have to substract it  from the considered Fres . And because the air resistance is the same for both sleigh, you need to take a bigger percentage from Fres,b than from Fres,a.

So with the example that Ma  = 2Mb and v is the same, you get:

  • For bobsleigh a: Fres,a,new = Fres,a,old – Fa = 2Fres,b,old – F

And a = F/M = (2Fres,b,old – Fa)/2Mb = Fres,b,old/Mb – Fa/2Mb.

  • For bobsleigh b: Fres,b,new = Fres,b,old – Fa .

And a = F/M = (Fres,b,old – Fa)/Mb = Fres,b,old/Mb – Fa/Mb.

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.

Start of the USA women 2 persons bobsleigh

Starting of a bobsleigh race. Image: Tim Hipps

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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WTF Simon

WTF Simon

Runner, Physicist, Dutch 3000m steeplechase champion, day-dreamer, sport minded and science lover
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