# Air in front of a cyclist hiding behind other cyclists

All sources I have been reading say that a cyclist hiding behind other cyclists can use up to 30% less power to keep the same velocity as the front cyclists. I understand that the front cyclist has to 'break' the most air resistance, but what exactly is it that makes it easier for the cyclist behind. Of course, it's not vacuum, the air is still there that the back cyclist has to face but is it less dense? or what exactly makes it easier for a back cyclist to flow through the air? That's assuming for the sake of the argument that there's no strong head wind.

There is not really a simple answer.

That the second cyclist uses less power to go the same speed has been shown many times, but the effect depends on the speed of both riders, the position of their body on the bike, and the distance in between them. There does not seem to be a simple mathematical way to describe the effect, so here are some images from computational fluid dynamics simulations:

The general and admittedly vague consensus is that the trailing rider benefits from the low pressure area behind the lead rider. The drag force $F_D$ is given by:

$$F_D\ =\ \frac{1}{2} \rho v^2 C_D A$$

where
$\rho$ = density of fluid in $kg/m^3$
$v$ = speed of object relative to fluid in $m/s$
$C_D$ = drag coefficient (unitless)
$A$ = cross sectional area in $m^2$

It is not a tractable enough system to be modeled by slight modification to the above equation e.g. a lower speed relative to the fluid for trailing rider, a change in the effective cross sectional area/drag coefficient/fluid density, or a "tailwind" behind the trailing rider.

• If d=0.01 m = 1 cm as the figure claims, it looks unrealistic as I'd suspect there would be very little space to have them seem to be 2 objects instead of 1 larger one. Are the numbers off, or can you explain? Commented Aug 21, 2017 at 1:26
• @BobBee 1 cm is the distance between the back wheel of the front bike and the front wheel of the back bike Commented Aug 21, 2017 at 1:40
• Ok, thanks. Hard to get it tighter. The figures then look like there's little difference on the front and back rider. Can you say what is the math relationship between pressure coefficient, and drag coefficient or anything related? Commented Aug 21, 2017 at 3:09

Since you can't go through air molecules, in order for the first cyclist to move through the air he has to "push" all those molecules out of the way. The only reason there isn't a vacuum behind him is because air molecules are so quick to fill in the void.

Since the "void" (not quite a vacuum) he's creating is moving forward, air molecules that move in to fill it keep moving in the direction in a nice little pocket behind the biker (he's dragging air behind him, hence the name "drag"). This creates the equivalent of a tailwind for anyone in the "pocket".

• Thanks - am I correct in understanding that the quicker they all ride, the more efficient this pocket is? Commented Aug 20, 2017 at 20:41
• @Señor O do you have a source? Commented Aug 20, 2017 at 21:01

Senor O gives a plausible and qualitatively correct picture of events, but his terminology is way off. Nothing remotely like a vacuum occurs.

Under standard conditions the pressure in the atmosphere is about $10^5$ pascal $=10^5 kg.m^{-1}s^{-2}$. An object of any kind moving through air having density $\rho$ with velocity $U$ creates pressure changes of the order of the dynamic pressure $1/2\rho U^2$. Taking a density of $1.3 kg.m^{-3}$ and $U=10m.s^{-1}$ gives about $6.5$ pascal, or a change of less than one-hundredth of a percent.

Because we are continuously exposed both internally and externally to the enormity of the atmospheric pressure, we are not aware of it, but it sure tales a lot of effort to produce a vacuum.

• Can you read? "The reason there isn't a vacuum..." Commented Aug 21, 2017 at 2:19
• Yes, I can read and that is exactly why I responded as Idid. The reason there isnt a vacuum is that we are a factor of about ten thousand away from any situation where a vacuum might appear. In developing a sound physical intuition it is very important to have a feel for the orders of magnitude involved. There are indeed situations where flow past a body does create a near vacuum behind it. They occur when space vehicles reenter the atmosphere. It helps to understand the difference. Commented Aug 21, 2017 at 3:52
• You're making absolutely no sense. I never said anything to the contrary of what you just said. Commented Aug 21, 2017 at 20:30
• Well, to my mind, you did. In choosing to speak of a "void" that is "not quite a vacuum" you create a mental image that is very inappropriate. I just want to reserve strong language for situations that justify it. It is easy enough to get confused by fluid behavior. Commented Aug 21, 2017 at 21:13