By Bob Howland
After a recent windy ride, Premium Member Bill Rosenfeld wrote to pose two questions about the physics of riding in the wind:
1) When you’re buffeted by a cross-wind, does going faster make you more or less stable?
Velocity is a vector quantity; it has both speed and direction. Let’s say you are going directly north (0 degrees) at 20 mph and you are being hit by a steady direct perpendicular 30 mph cross-wind at 270 degrees West (the wind is coming from your left at a 90-degree angle).
Then, from Pythagoras’ Theorem, you are being pushed by a diagonal cumulative velocity of the square root of (20 squared + 30 squared) = 36 mph. The angle of this velocity to you is tan-1 (20/30) ~ 34 degrees above your right 90-degree East direction, which is ~ 56 degrees NE, compared to 0 degrees North.
What this means is, if you were to go airborne to bunny hop a road obstacle, you may find yourself coming down with a new direction of motion that may not agree with your front tire. In short, your new direction of motion might be somewhere around 56 degrees NE (or compared to your 0 degree original heading, this would be diagonally ~34 degrees above your right), because That’s the cumulative effect of the velocity of the cross-wind from your left, and the velocity of your travel — North at 20mph and that perpendicular side wind of 30 mph from the West.
The faster you go, or the faster the side wind, or both, it is highly likely you will be less stable, likely in a surprising diagonal direction, than if you are tooling along at 14 mph.
All bets are off if the wind gusts to 40-60 mph — because air has mass that introduces 2 new significant vector quantities, momentum and force. Moving air has mass and velocity. Further, since the air mass is gusting or accelerating as a wind, and force = mass x acceleration, if you get hit with a gusting side wind similar to the scenario above, it simply makes that above scenario worse, causing new momentum and force vectors pushing you in surprising new directions.
You may feel yourself being pushed sideways, real hard, into a new line that on some roads may be extremely dangerous. The race up Mt. Washington has had many cases of riders being knocked off bikes. I personally have been bombing down roads in the mountains west of Ft. Collins, Colorado, at about 40 mph, have swept turns into crosswinds of approximately 40-50 mph and had the bike jump 2-3 feet (nearly 1m) laterally.
I was actually sliding across the road, holding the bars in my direction of motion as if I was on a motorcycle sliding around a turn. I would guess my diagonal vector at around 55 mph would have been about 30 degrees or so above my direct right. Frankly, it was pretty scary.
I slowed WAY down, grabbing the brakes and heating up the rims. But I felt safer going about 20 mph when those side winds repeated around other turns.
Going slower increases your downward gravity vector, thus increasing your tires??? bite into the pavement, and from that increased friction, hopefully overcoming any side vectors due to wind.
So, to answer the original question, going faster when buffeted by a cross-wind makes you LESS stable. Going slower makes you more stable, able to lean into cross-winds, have time to adjust and steer, and thus control your destiny.
2) When riding into a headwind, does going faster make it harder? Is the relationship linear or worse?
I did some research and found this equation:
Force of drag = 1/2 x D x V^2 x Cd x A
D = The density of air.
V = The relative velocity of air hitting the object (^2 means squared).
Cd = The drag coefficient.
A = The area exposed to the wind.
That squared velocity is the literal drag on trying to go faster into the wind. It doesn’t get harder as a direct relationship, it gets harder, SQUARED.
If you are going 15 mph into the head wind, you have some drag force (with no units of measurement, so let’s say it is “15”.) But if you accelerate to 20 mph, a 5 mph increase, your new drag force is 5 squared = “25” above where you started at 15 mph.
Since you started at a drag force of 15, then 15 + 25 = 40, which is the new force being exerted on you by the wind when you are moving along at 20 mph. (This assumes a steady headwind; of course, as the headwind increases, so does the drag force — again, at much more than a linear progression.)
Of course, you must overcome (or best deal with) this drag force by muscle strength and technique (your best, most aero position on the bike) — and you may be helped by an aerodynamic bike as well.
So, to answer the question, YES, going faster into a headwind makes it harder. And the relationship is not linear; it is “worse” — drag force into a head wind increases as the SQUARE of your velocity increase.
Bob Howland is a physics teacher in Florida. He’s also written on paceline physics and the physics of aero wheels for RBR.