Imagine a human running on a treadmill with wind present. Perhaps someone set up a fan pointed at the runner’s front (or back). Perhaps the treadmill is outside. Your pick.
My question: do headwinds/tailwinds make running on a treadmill more difficult/easier in a manner similar to running outside?
Here are a few earlier human-on-a-treadmill threads, but I didn’t see this question answered clearly:
Yes.
The wind is pushing you backwards and so is the treadmill, you have have to overcome both when running forwards, not just the treadmill.
Suppose you have a 10 mph treadmill and a 10 mph fan. Then, imagine yourself in the reference frame of a stationary treadmill surface. The air is then stationary as well. If you run forward on this surface at 10 mph, then you’ll get the same 10 mph headwind as you would on the ground in still air. That’s in contrast to the normal treadmill case where you don’t experience the headwind.
Technically, the treadmill isn’t pushing you back at all. You could have frictionless wheels and stay in place indefinitely by just rolling forward. It’s the inefficiency of running (energy absorption in the shoes, etc.) that provides the resistance.
The record for a human-powered bicycle is >180 mph. But it was behind a racecar with a huge cowling that blocked the wind. Essentially the same as a treadmill (with no fan).
Edit: Sorry, I initially thought you were disagreeing with me here now I see you weren’t.
By the same logic, which I agree with, when you are running on the treadmill without a 10 mph fan, in the reference frame of the treadmill you have a 10 mph tail wind, hence it’s easier without the fan.
Of course it is. If you don’t run or walk on the treadmill then you will stay stationary in its reference frame or be moved backwards in the reference frame of the room it’s sitting in.
If you have frictionless wheels you would only be moving forward reference the treadmill if you started out moving forwards reference the treadmill. If you started out motionless in the treadmill’s reference frame then you will stay that way, i.e, you will be moving backwards.
That’s all needlessly complicated though, you don’t have frictionless wheels, you have a solid friction surface between your shoes and the treadmill’s surface and the treadmill is pushing/pulling/moving (however you wish to think of it) you backwards in the room’s reference or holding you in place in the treadmill’s reference.
To keep it all to one frame of reference:
Treadmill’s frame of reference (the running surface).
The running surface is stationary. You run forwards at 10 mph. There is a 10 mph tailwind so you feel no wind, and get hot and bothered and wish there was a fan.
So, you get a big industrial fan and put it in front of the treadmill.
Now the running surface is stationary. You run forwards at 10 mph. There is nil wind reference the treadmill surface because the fan is pumping out air at the same speed the treadmill is moving backwards but there is a 10 mph wind relative to you, that you have to push in to. Hence, it’s easier without the fan. By your own logic at the start.
Edit: Treadmills and escalators seem to confuse the hell out of people because the moving part, and therefore the relevant reference frame, is so small compared to the world they exist in that even when trying to think in the appropriate frame of reference it’s easy to let the other reference creep in.
When trying to figure out the effects of certain parameters, it’s often instructive to take them to an extreme. In the present case, imagine two scenarios:
A: walking on a treadmill with no fan, and
B: walking on a treadmill with an industrial fan hitting you with an 80-MPH wind.
In the first scenario, you have zero wind resistance; the only real mechanical work you are doing is propelling each leg forward every time you take a step. In the second scenario, not only are you working to swing each leg forward, but your planted foot is also exerting a large forward force (maybe 80-90 pounds?) to maintain your body’s position in the gym even as the tread belt is retreating to the rear. If you were walking outside in an 80-MPH headwind, the mechanical work your legs do would manifest as in increase in your potential energy as you move yourself upwind. On the treadmill in the wind, you aren’t moving upwind; instead, the mechanical work your legs do manifests either as heat in the treadmill’s dissipative device (e.g. an eddy current brake) or as electrical power sent back to the grid. With this gigantic headwind, the large drag force makes it obvious that aero drag does make a difference.
But how much of a difference does it make at realistic running (and wind) speeds?
A casual bicyclist (for whom aero drag consumes virtually all of their pedal power) needs to hit about 20 MPH to get a good aerobic workout. OTOH, a casual jogger need only hit 7 MPH to get the same aerobic workout. The aero drag power (not force) at 7 MPH is about 4% of what it is at 20 MPH (you could even double that to 8% because the runner isn’t in the same aero tuck as the rider). Consequently, aerodynamic drag is a relatively minor energy sink for running. Instead, it’s the swinging of your limbs that demands most of your power output. Every time you use your muscles to accelerate your arms/legs forward or backward, you’re doing mechanical work, burning cellular fuel to make it happen. When you use your muscles to decelerate your limbs, your muscles are receiving mechanical work, but that work doesn’t get converted back into cellular fuel; it gets pissed away as internal heat. A limb that’s moving at a higher speed has more kinetic energy than one moving at lower speed, and a limb that’s being cycled more frequently has a bigger power requirement than one that’s being cycled less frequently. If you want to run at 14 MPH instead of 7 MPH, the peak velocity of each limb will be twice as high, meaning four times as much kinetic energy in them during each swing. But you’ll also be swinging them twice as often. Unless I’m figuring things wrong here, it looks like doubling your running speed means you need 8 times the power, disregarding any aero drag. But aero drag power increases as the cube of speed too, so the percentages are the same regardless of running speed.
The upshot of all of this is that for a runner on a treadmill, blasting them with a whole-body wind that matches the tread belt speed might be expected to increase their power requirement by 8%.
Thanks, @Richard_Pearse, @Dr.Strangelove, and @Machine_Elf.
The impetus for me to ask is because I am thinking of setting up a fan by my treadmill. The main purpose will be to increase comfort. But then I got to thinking about the various effects as a physics puzzle.
Combining my reading of the earlier threads (linked in my OP) and your responses, my thinking quickly evolved along these lines:
One of the previous threads mentioned setting one’s treadmill on a 1% incline to help compensate for missing wind resistance. (Of course, someone else produced a cite that said this is bunk… but then this is running, where there seems to be a million different opinions on every little thing.)
Anyway… I think I’ll try a combo of fan-in-front + 1% incline and see how I like that.
It is very rare that I use a treadmill but I do have a trainer bike setup in my bedroom that I use frequently and I can’t stand doing exercise without a fan. If I were you I’d definitely go with a fan. I’d hazard a guess that any performance lost by running into a small headwind would be well and truly offset by having your body at a good temperature.