# Aerodynamics of cycling into a tail wind

I was looking at Steve Gribble's Cycling Calculator , and I noticed that the aero resistance was higher going 40 mph with a 20 mph tail wind than going 20 mph with no tail wind. Why is this? I always thought they should be the same.

Think about the spokes: when you're going 40 mph, the spokes near the tops of the wheels are moving at 80 mph, so moving through the air at 60 mph. Meanwhile, when you're going 20 mph in still air, the spokes near the top of the wheel are only moving through the air at 40 mph. It is true that in the case with a tail wind, the air actually puts a forward force on the spokes near the ground, but it does not fully cancel the extra drag from the the spokes near the top--drag increases faster than linearly with speed.

• Just to clarify, are you saying that they would be the same if I had a magical floating bicycle with no spinning wheels? – Aperson123 Nov 26 '18 at 22:32
• Yes, as far as air resistance goes, the only difference between the two cases is the wheels. – Ben51 Nov 27 '18 at 0:50
• I just realized this answer is wrong, look at the answer to this question: physics.stackexchange.com/questions/137144/… – Aperson123 Nov 27 '18 at 1:49
• It’s not wrong. That’s a different case. You didn’t ask about the energy required to maintain each speed, you asked about the air resistance: the force. – Ben51 Nov 27 '18 at 1:52
• The discrepancy in the cycling calculator I'm talking about is explained by that answer. Note that I didn't explicitly ask about force, and the cycling calculator actually gives the power needed to overcome the resistance. – Aperson123 Nov 27 '18 at 1:56

The drivetrain loss and rolling resistance depend on your speed relative to the ground, and are higher at 40 mph than at 20.

In the calculator, if you set the drivetrain loss and the coefficient of rolling resistance to 0, and a tailwind of 20 mph, you will see that it does calculate that zero power required for a velocity of 20 mph. For velocities less than 20 mph you need to use your brakes, since the wind force is trying to make you go faster not slower.

• This is correct, but it doesn't answer my question. Set rolling Resistance to 0. With no tail wind, it says it takes 17.56 watts to go 10 mph. With a tailwind of 50 mph, it takes 105 watts to go 60. Why is there a difference? That's the question. – Aperson123 Nov 26 '18 at 22:11