# Forget planes on treadmills, here's a sail-cart out-sailing the wind!

It’s pretty well established that you can tack an ice-sailboat in a fashion that allows you to travel downwind at rates faster than the wind, but conventional thinking has it that you can’t exceed windspeed with your sailing vehicle pointed directly downwind. These guys beg to differ.

Took me a while, but eventually I saw how the thing works - the prop doesn’t drive the wheels, but is driven by them. Because it’s blowing into the tailwind, it can provide enough thrust to accelerate even after the vehicle is moving faster than the wind. Eventually it will reach some point where the air and rolling resistance are in equilibrium with the extra force resulting from the air/ground velocity differential, but if you’ve got the prop designed and geared right, that should always be at a speed higher than the wind.

I want one.

That’s so counterintuitive it makes my brain hurt.

Yeah, I’m really struggling to see how the force generated by the wheels turning the prop can possibly be greater than the force needed to turn the wheels in the first place, magic gearing or not. :dubious:

So what drives the wheels?

The vehicle moving over the ground, which it does because it’s being driven by the wind. As jjimm says, it’s very counter-intuitive.

As it initially accelerates from rest, the vehicle behaves as a crude sail. The wind pushes on it, and it moves forward. Obviously this force alone can never push it faster than wind speed minus losses from rolling resistance. However, as it rolls, the driveline between the wheels and the prop force the prop to spin. The prop, however, is pushing on air that’s moving at a different speed than the ground relative to the cart.

Take the case where the cart is moving at precisely the speed of the wind, which we’ll suppose to be 10mph. At this speed, the prop is from its perspective in dead air. However, wheels are driving it to spin, so it provides thrust, which will accelerate the cart unless there are sufficient counteracting forces to balance it. Those counteracting forces - air resistance, which in the case of moving at 10mph is nil, rolling resistance, which for lightweight carts on bicycle tires is negligible at 10mph. And the biggy, the friction losses in the driveline. But if the sum of those forces is less than the thrust being generated by the prop, the cart will accelerate until equilibrium is reached. As the cart accelerates, the prop spins faster and faster, and so provides more and more thrust, but that thrust will be increasing counteracted by rolling and especially air resistance. This doesn’t make it a perpetual motion machine - it’s harvesting energy from the difference between groundspeed and airspeed. Stop the wind (or the ground, in the case of the demo videos showing a model on a treadmill in dead air) and the cart will stop. It requires the difference between air and ground speeds to operate.

Again: how is the prop generating more force than the force being applied to the wheels? The latter is certainly applying braking force to the vehicle…

The prop isn’t generating more force than is being applied to the wheels. Because of the tailwind, it doesn’t need to. The force available at the wheels is dependent on groundspeed. The force required to accelerate the cart is dependent mostly on air resistance which will vary with airspeed, not groundspeed.

There are much better explanations than I can manage in the comments in the linked article, including at one point a published, peer-reviewed article which gives you all the relevant math if you’re so inclined.

Giving the concept the benefit of my doubt for now, just what part of the vehicle is being driven by the wind? The frame? The rim of the wheels? The propellor?

If the latter, with wind pushing on the propellor, which spins and drives the wheels…wait a minute. I thought the wheels were driving the propellor. Is the propellor simultaneously being pushed by the wind, and pushing the wind as well? And if it doesn’t push the wind, how does it work?

Somehow this reminds me of the sailor who mounted an electric fan to blow his sails, and the electricity was supplied by an onboard wind generator. Now if only he could have avoided all the losses in the system, he’d have a nifty idea, but somehow the conversion percentage never exceeded 100% (or even came close). Wonder why.

If this concept works, why not put an extra propellor on an (prop-type) airplane, powered by the wind? Then, once airborne, you could draw power from that unit to power the main propellor?

You suggested we consider the case where the cart is effectively in still air. Very well, let’s do so. There is therefore no net force on the cart from the wind, and no air resistance either. We will assume no rolling friction. But the wheels aren’t turning for nothing - they are coupled to a mechanism that is being made to do work. The mechanism can’t generate energy from nothing. Nor can it generate more than is being put in to the wheels. If the prop is not generating more force than is being used to turn the wheels, there is no net acceleration. The cart is not going to go any faster.

is utter bullshit.

Again, the energy is coming from the difference between air and ground speeds. The ground drives the wheels which drive the prop. This is fundamentally no different than a conventional sailboat moving faster than windspeed by sailing perpendicular to the wind, except that it uses a different physical mechanism to leverage the difference in speeds. On an airplane, of course, you only have one medium that you’re traveling through so you can’t leverage speed difference.

Here and here are mathematical analyses of the problem for those with sufficient math skillz to follow along. (Both links are pdfs)

This. A thousand times, this.

I’m still trying to get my head around this, but it seems as though their claim may be sound - because a windmill-driven vehicle can drive directly UPwind under wind power - seems to me that these two possibilities are related.

Except that the case they’re claiming is more or less opposite - supposedly the vehicle’s momentum transferred via the wheels to the prop generates thrust, enough to overcome the braking force that this same process applies to the wheels.

Malacandra, your skepticism (healthy btw) appears rooted in your misunderstanding of the claim. The ‘momentum transfer’ statement you make above is not the claim and it doesn’t happen.

During acceleration and steady state operation, the key momentum transfer occurs between the vehicles propeller and the air.

Here is the claim: “Directly downwind, faster than the wind, powered only by the wind’ steady state”.

basics:

– the vehicle does not use stored energy to accelerate
– at all speeds the device is slowing down the wind relative to the ground
– the spinning rotor is a propeller, not a turbine
– the wheels provide the torque to turn the rotor (always).
– the rotor does not provide the torque to turn the wheels (ever).
– it is equipped with a fixed ratio transmission
– it will take off from a standing start on it’s own.
– there’s no "null point’ of any sort at windspeed.
– It will maintain a speed well above wind speed indefinitely
– by design, this particular one works best when aimed directly downwind.
– one can be built to go faster than the wind in any direction
– a simple gearing change will cause it to go directly upwind rather than down

JB

Thanks JB, I did follow the link and read - or at any rate skimmed through - the discussion, and I understand what the claims actually are: specifically, that the wheels turn the prop. I’m struggling with the one key point, however: that the prop can generate more thrust than the drag imposed by forcing the (otherwise frictionless, let’s assume) wheels to do work on the prop.

I grasp that this is not a perpetual motion machine if in fact the airstream is losing energy (similarly, in the case of the treadmill experiment, it can presumably be shown that the treadmill is drawing more current as the speed of the cart increases) but you’ll understand that I am deeply suspicious as to how this miracle is supposed to happen.

Thank you for registering to explain this.

No problem Malacandra.

There’s nothing unhealthy about your skepticism. It’s a brainteaser that screws with your intuition in a variety of ways.

Give me a few minutes and then check back – my next post will be a energy/force balance analysis that will answer your above question.

Thanks for sticking with it.

JB

Dude, this googling yourself and obsessively arguing your case isn’t healthy!

Thanks for dropping in, though. I spent a good long time last night watching those videos and thinking “That just can’t work” before the mechanism started making any sense. Regarding an upwind vehicle, though - you say a simple gearing change is sufficient, but don’t you have to run the drive mechanism in reverse, i.e. with the prop powering the wheels? My understanding of this machine is that you take the mechanism coupling the vehicle to the medium with the higher relative velocity, and you use it to transfer energy to the mechanism coupling the vehicle to the medium with the lower relative velocity.

Dang, just when I think I have things figured out.

Thanks for bringing to our attention this incredibly interesting subject, Gorsnak !

The following treatment answers the question that Malacandra asked above regarding the power demands the propeller places on the wheels.

Notes:

1: The even 1.0hp number used below was chosen for ease of explanation. The actual HP numbers are dramatically higher on the Blackbird. The principles of course scale without issue.

2: For illustrative purposes, let’s take our DDWFTTW vehicle and remove the chain drive that links the drive axle with the prop shaft and replace it with a generator on the drive axle connected to an electric motor on the prop shaft.

3: Initially in the treatment we will ignore all losses in the system. This is just for ease of illustration. I will address the real world losses (which always exist) near the end of the post.

Alrighty – following is a simple energy/force analysis for a small propeller equipped DDWFTTW vehicle. In this analysis, we show that in a 27.5ftsec (~20mph) tailwind, and with the vehicle traveling DDW over the ground at 55ft/sec, the retardant force on the wheels needed to drive the propeller is less than the propeller needs to keep the vehicle at that speed.

A:
1.0 HP = 550 foot-pounds per second
(http://en.wikipedia.org/wiki/Horsepower)

This means that if we have 10lbs of force exerted on our chassis pulling it downwind @55ft/sec, we can harvest 1.0hp from our wheels with our lossless generator. (we’ll deal with losses below)

B:
1/2HP = 275 foot-pounds per second
This means that at 27.5ft/sec, 10lbs of force can be produced by a lossless propeller consuming 1/2hp. (we’ll deal with losses below)

C:
If the wind is blowing at 27.5ft/sec and our vehicle is traveling DDW at 2x the speed of the wind, the vehicle is traveling over the ground at 55ft/sec and through the air at 27.5ft/sec.

D:
Through the establishment of “A”, we know we can pull 1.0 HP from the wheels of the vehicle if it’s propelled by 10lbs of force, and through the establishement of “B” we can see that the propeller in the relative tailwind only needs 1/2HP input to produce that same 10lbs of force.

E:
We subtract the 1/2hp that the prop needs to produce its 10lbs of thrust from the 1.0hp that the wheels can produce from that same 10lbs and you have 0.5hp left over for the system losses.(told you we would get to losses).

In the real world we don’t have lossless components of course. If you consider an 85% efficient propeller (easy to achieve) and an 85% drive train (even easier to achieve with chain drive) we’ve still got nearly 1/4 HP left over for the Crr of the tires (very low for high pressure bike tires) and aero drag (which is also very low as our relative headwind is slight).

Do the same calcs on a no wind day and it’s easy to see that the wheels still produce 1.0HP at 55ft/sec, but now the propeller is forced to do work at 55ft/sec rather than 27.5ft/sec and it now takes a full 1.0HP at the prop to produce the 10lbs of force. This of course means that there is nothing left for losses and since there are always losses, the vehicle simply can’t motivate itself when there is no wind.

Malacandra, the short version of the above is this:

In a the above tailwind, the vehicle is moving over the ground twice as fast as it’s moving through the air. Using simple work=force/distance calculations it can be seen that this means the wheels can produce twice as much power as is needed by the prop to maintain that 2x speed.

This differential between the speed over the ground and speed through the air is of course the key to the entire brainteaser.

JB