Hoping someone can help my intuition around speed in different wind conditions.
On Bike calculator, I’ve taken two cases, 20km/h speed + 20km/h headwind, vs. 40km/h speed + 0 km/h head wind. Since at 40km/h most of the watts is fighting aero drag, I would have thought these would require similar watts? But it shows 186 W (manageable for many) vs. 373 W (big watts)
I would have assumed that these would be much closer, since in both cases you’re (mostly) fighting 40km/h of air-drag, irrespective of the speed across the ground?
You’re right, about 8W to go 1km/h in a 39 km/h headwind.
Interestingly this calculator breaks it down a bit, giving you the force (Newtons) the air is placing on you. Using the calculation Work = Force x Distance seems to be the calculation, but the problem here is that the distance being used is along the ground, so if the speed is low the distance/time is low so the work/time is also low, but doesn’t it make more sense to consider distance relative to the air?
I’m not sure I agree, my thinking is work done against the wind is relative to the air is not relative to the ground. In the OPs situation 20km/h speed + 20km/h headwind you are moving through 40km of air every hour even though you are only travelling over 20km of ground.
Powerdrag wind = 0.5 * CdA * Air density * (Speed+ Headwind Speed)^3
Edit: what difference does it make when you’re on a treadmill
My initial reaction is no… but it’s been 25-30 years since I did these kinds of calculations as a student / engineer :).
Power = Force * Velocity.
In the OPs question:
Force is calculated based on the 40 kph ground speed + headwind
Velocity is calculated relative to ground speed of 20 kph
So riding at 20 kph into a 20 kph headwind will have the same aerodynamic drag force as riding at 40 kph. But the power required to overcome aerodynamic drag will be lower as the ground speed is lower.
Pulled up an early morning windless (rare!) ride - 20m effort, 12.5km, 37.4kmh at 216W Avg/217W NP (64kgs). That’s without trying to be aero, just a tempo morning cruise. Same ride - 11m effort, 7.5km, 41.4kmh at 246W Avg/246W NP. Went as aero as I could for that one. Achievable
I see some of what you are saying. The key in your response I think if I understand it correctly is power is the rate of doing work. In this case if the object (a cyclist) does not move then no work is performed since it must move for there to be a rate of work performed it has to move. The part that got me was the fact it takes 2x as long to do the 30 km therefore the work is the same but quite a bit less power (rate of doing work) is needed to to get there in 90 minutes vs 45 minutes.
Assuming you could conjure up enough magic to keep yourself upright while clipped in with no forward momentum and no track stand, you’d likely find 40kmh headwind will overcome the rolling resistance and get you moving, albeit slowly. So yeah, the power needed to stand still at 0kmh with 40kmh winds would most definitely be >0W.
The ask was what it took to stand at 0kmh in a 40kmh wind, and answer was 0W. I took as implied that brakes would not be used, but if they are then I’ll concede it is 0W. Otherwise you’ll most definitely need more than 0W to stand at 0kmh in a 40kmh wind … or you will be moving, and therefore not at 0kmh.
This is where my high school physics has let me down. Power = torque + cadence, but cadence is 0. You’re expending energy, but not making power. I’ll stand silent in my shame corner now
As you move through a volume and make waves, those waves are being “stacked” up (for lack of a better term). The faster you go the more “scrunched” up they are… thus the “sonic boom” when you move past the speed of sound. I am curious if there is a difference with the thing moving through the volume (i.e. a car, jet, rider, etc.) compared to a force (i.e. wind) being pushed against it.
E.g. A rider in a wind tunnel with a 20mph wind blowing over them, vs a rider out on the road cycling in still air at 20mph?
I don’t think there is a meaningful difference in the aero drag they experience. There may be some small differences due to boundary layer differences (wind tunnel vs road) but I’d guess those are small.
if the object stays in one place and does not move then power by definition is 0. Work is the act of moving an object from one place to another in this discussion, and power is how fast it moves (ie the rate of change). If it doesn’t move then work is 0 and so is power. That is what RChung is saying. Because power is the rate of work, if you slow it down then you reduce the power the work being the same. In the OP example note it takes 90 minutes at 20 and 45 40, but the work (as shown by calories expended but by definition, you moved the same object the same distance therefore the work is the same). Thus there is less power in the slower scenario.
