# Wind Power Vehicle Traveling Down Wind Faster Than The Wind

by yn3
Tags: faster, power, traveling, vehicle, wind
 P: 11 Sorry to see this topic dropped. I was looking to seeing Yn3's maximum angle. Rumor has it that with it's fixed prop Blackbird functions best directly downwind. Any thoughts on that?
 P: 206 RCP, it's not the 'fixed pitch' nature of the Blackbird (which has gone DDWFTTW in both fixed pitch and variable pitch configurations) that makes it function best DDW, it's the circular nature of it's sail path. Fixed or standard 'variable pitch' makes no difference in it's off axis performance. Even if it were equipped with a 'cyclic pitch' hub, it would still perform best DDW -- but the off axis performance would degrade slower off DDW. But the you knew that already -- I'm just responding to the thread to answer your question on the record. JB
 PF Patron Sci Advisor Emeritus P: 6,203 Here we go again :-) As others said, you do not deserve your marks on mechanics 101 if you can't figure out that this is trivially possible to go faster than the wind. The elementary theory of it (of the order of an exercise of medium difficulty in said mechanics 101 course) has been posted several times and it is quite disturbing if people with a degree which should have mastered such a course cannot understand it almost immediately, worse, dispute it. You could just as well dispute that things heavier than air can fly. The long, locked threads cited earlier must contain about everything that can possibly be discussed about it.
 P: 245 I have read a dozen of pages on this topic but I cannot understand it. Could someone please explain it or give a link to an explanation? Isn't it true that once you are up to wind speed and use the wheels start to power the propeller, the energy will come from the kinetic energy of the cart and since the propeller cannot propel air at 100% efficiency some energy will be lost and shouldn't the cart slow down? I simply don't understand how it works.
PF Patron
P: 1,321
 Quote by chingel I have read a dozen of pages on this topic but I cannot understand it.
 Could someone please explain it or give a link to an explanation? Isn't it true that once you are up to wind speed and use the wheels start to power the propeller, the energy will come from the kinetic energy of the cart and since the propeller cannot propel air at 100% efficiency some energy will be lost and shouldn't the cart slow down? I simply don't understand how it works.
It's meant to be an exercise in aerodynamics. Break the problem down into a free body diagram and figure out if it is possible or not.
P: 563
 Quote by chingel I have read a dozen of pages on this topic but I cannot understand it. Could someone please explain it or give a link to an explanation? Isn't it true that once you are up to wind speed and use the wheels start to power the propeller, the energy will come from the kinetic energy of the cart and since the propeller cannot propel air at 100% efficiency some energy will be lost and shouldn't the cart slow down? I simply don't understand how it works.
If there was no wind, the cart would have to be 100% efficient just to maintain speed, which of course in the real world isn't possible. Since the air is moving wrt the ground, the thrust at the propeller only has to be a portion of what it would be if there was no wind. Given reasonable losses to friction and such, a properly designed cart is quite capable of doing so.

Did that help?
P: 245
 Quote by mender If there was no wind, the cart would have to be 100% efficient just to maintain speed, which of course in the real world isn't possible. Since the air is moving wrt the ground, the thrust at the propeller only has to be a portion of what it would be if there was no wind. Given reasonable losses to friction and such, a properly designed cart is quite capable of doing so. Did that help?
I can understand that the thrust has to be a portion of what it would have to be when there is no wind, but nevertheless, no matter how little thrust, it has to come from the kinetic energy of the moving cart, I would think. Then the propeller uses some of that energy to accelerate air particles in one direction which accelerates the cart in the other direction. Isn't it true that the propeller cannot accelerate air particles with more force than it is getting from the wheels? What am I missing?
 P: 71 A simple wikipedia search would have given you all the answers http://en.wikipedia.org/wiki/Sailing..._than_the_wind The formula and maths etc ... everything its all there!
P: 563
 Quote by chingel I can understand that the thrust has to be a portion of what it would have to be when there is no wind, but nevertheless, no matter how little thrust, it has to come from the kinetic energy of the moving cart, I would think. Then the propeller uses some of that energy to accelerate air particles in one direction which accelerates the cart in the other direction. Isn't it true that the propeller cannot accelerate air particles with more force than it is getting from the wheels? What am I missing?
You're forgetting that the thrust at the prop can be higher than the drag at the wheels but only because the ground is moving past the cart faster than the air. If there is no wind, the air is moving past the cart at the same speed.

The cart essentially gears down the force at the wheels and turns the prop slower than the ground speed but with more force against the air.

The drag at the wheels is x, the speed across the ground is v; since the prop is acting on the air, with no losses, the thrust from the prop can be 2x when it is turning at a rate to move the air back at half the ground speed (v/2). Same principle as a lever; the force at one end can be much greater than at the other but the distance is less.

Better?
P: 563
 Quote by Uglybb A simple wikipedia search would have given you all the answers http://en.wikipedia.org/wiki/Sailing..._than_the_wind The formula and maths etc ... everything its all there!
But even with all the answers, sometimes it has to be explained in the right order and the right way for the light bulb to go on.
P: 245
 Quote by mender You're forgetting that the thrust at the prop can be higher than the drag at the wheels but only because the ground is moving past the cart faster than the air. If there is no wind, the air is moving past the cart at the same speed. The cart essentially gears down the force at the wheels and turns the prop slower than the ground speed but with more force against the air. The drag at the wheels is x, the speed across the ground is v; since the prop is acting on the air, with no losses, the thrust from the prop can be 2x when it is turning at a rate to move the air back at half the ground speed (v/2). Same principle as a lever; the force at one end can be much greater than at the other but the distance is less. Better?
I'm sorry I do not understand how. How can the thrust be higher than the drag at the wheel? Aren't they are mechanically connected? Move air back at v/2 relative to what, the cart or the ground? If you use gears to make the propeller move faster than the wheels, it will displace more air but also drag the wheels more, because it does more work and needs more energy, if you make it spin slower it provides less acceleration but also causes less drag, at least the way I understand it.
P: 563
 Quote by chingel How can the thrust be higher than the drag at the wheel? Aren't they are mechanically connected?
Thrust is a force, and drag is a force. You do know that by using a lever or gears, you can put x amount of force into one end and get 2x, 3x, or 10x force out of the other end right?

Gears are mechanically connected yet change the amount of force put in at one end to a different force at the other; no magic, just leverage or mechanical advantage.

 Quote by chingel Move air back at v/2 relative to what, the cart or the ground?
Relative to the cart.

 Quote by chingel If you use gears to make the propeller move faster than the wheels, it will displace more air but also drag the wheels more, because it does more work and needs more energy, if you make it spin slower it provides less acceleration but also causes less drag, at least the way I understand it.
But we use gears to slow down the propeller, displacing less air but supplying more force for the same amount of work taken from the wheels.

For the sake of clarity, let's take losses out of the picture for a moment.

The wind is blowing at 10 mph. The cart, without the propeller engaged, gets pushed up to 10 mph. The pitch of the prop and the gearing of the cart is set up to push air back relative to the cart at half the speed of the wheels. The prop is engaged; the air around the cart gets pushed back at 5 mph, half the speed of the wheels. Since the force at the wheels is geared down, the force at the prop is twice as much as the drag at the wheels and the cart accelerates. F=MA so if the net force acting on the cart is positive, as it is so far, the cart will accelerate.

The cart gets to 15 mph; the prop is now turning fast enough to push air back at 7.5 mph and the force at the prop is still higher than at the wheels, so the cart will still keep accelerating. About now you're thinking that if that is true,the cart will keep accelerating forever; it won't, because the gear ratio determines the top speed in accordance to the speed of the wind.When the cart gets to 20 mph, the prop is pushing air back at 10 mph and the wind is still blowing at 10 mph, meaning that the prop is no longer exerting any force on the air, it's just freewheeling. With this gear ratio, the absolute best the cart can travel across the ground is twice the speed of the wind.

Now the wind drops to 7.5 mph; what happens to the cart? At 20 mph, it is still pushing air back at 10 mph but with the wind at only 7.5 mph, that means that instead pushing air back, it is actually trying to drag air forward at 2.5 mph. The net force acting on the cart is now negative, so the only thing that can happen is that the cart will slow down. What speed does it stabilize at? Again, twice the speed of the wind, or 15 mph.

Gearing the wheel speed down by half (0.5) to power the propeller gives a theoretical top speed of twice the wind speed. A different ratio will give a different theoretical multiple of the wind speed. Gearing the cart down less means the prop is spinning faster but with less force; it has the potential to faster for the same wind speed but it needs to be more efficient because the prop is supplying less force than before to overcome the real world losses.
 P: 11 @mender: I always like your basic explanations for how the cart works best. Find them reassuring in terms of how I perceive it. (And I wouldn't confess this elsewhere for fear of casting doubts on your understanding. ) I know it's in the blog somewhere, but bet you know the gear ratio of BB. What was it again? And using your explanation above, what would be the max BB could maintain steady state above ws? I may have seen this laid out many times before, but after 4k pages of such forgive an old guy if it overloads my RAM. The info is there, but often inaccessible. After much thought I can finally envision BB leaving the packing popcorn in the dust. With spork on board we are talking about over 600 lbs.. Couldn't it store a lot of momentum under the right conditions getting up to ws? If a tin can will exceed ws for a few seconds in a lull after a gust, wouldn't BB be capable of doing so for ten seconds or more? I'm speaking hypothetically above, as I know the NALSA rules take gusts and direction into consideration. But it was a first of its kind test for a sport's club, so might it not be in the realm of possibility they got some things wrong? I would still love to see how I Ratant's cart would do on a treadmill after seeing that popcorn sail past it in natural wind. And remember, he was clever enough to design a cart that had remote steering and could ride the wind without needing a guide wire.
 P: 245 Thank you for your explanations. Here is where I still have a problem. Doesn't energy matter also? Yes we can use gears to multiply the force, but doesn't the energy stay the same? Eg isn't the energy you put into at one end the same what you get from the other end, no matter what gears you use between? Otherwise you could just connect some gears to a wheel and then connect it to another wheel and multiply the force. You could do that, but doesn't the energy stay the same? To me it seems that it takes a certain amount of energy to make the propeller move the air and that energy can only come from the kinetic energy of the cart, no matter what gears you use. If you use gears to make the propeller slower, the force at the wheels is lower, but since they move more in the same time, don't they expend the same amount of energy as the propeller gets?
 PF Patron P: 2,949 The air stream 'moves' the propeller more than the other way around. Or, in terms of energy, the propeller takes kinetic energy from the air stream and converts it to the kinetic energy of the platform.
P: 563
 Quote by RCP I know it's in the blog somewhere, but bet you know the gear ratio of BB. What was it again? And using your explanation above, what would be the max BB could maintain steady state above ws? I may have seen this laid out many times before, but after 4k pages of such forgive an old guy if it overloads my RAM. The info is there, but often inaccessible.
IIRC, the advance ratio is 0.8, and to get the theoretical top speed, you use this formula: 1/(1 - advance ratio). So for BB it would be 1/(1 - 0.8) or 1/0.2, which is five times the speed of the wind. Speaks pretty highly of the team when they managed to get runs in the 70% of TTS (theoretical top speed) range with their first vehicle on their second outing.

 Quote by RCP After much thought I can finally envision BB leaving the packing popcorn in the dust. With spork on board we are talking about over 600 lbs.. Couldn't it store a lot of momentum under the right conditions getting up to ws? If a tin can will exceed ws for a few seconds in a lull after a gust, wouldn't BB be capable of doing so for ten seconds or more?
So if a heavy tin can could beat the popcorn just by being at ws when the wind dies slightly, why do you have a hard time visualizing BB beating the (maybe) 10 mph popcorn when it is going almost 20 mph faster even without the wind dying? The only chance the popcorn (or a leaf) would have of beating a DDWFTTW vehicle is if a sudden gust of wind propelled the popcorn (or leaf) to speed before the cart has a chance to accelerate, making the BB's momentum a disadvantage.

 Quote by RCP I would still love to see how I Ratant's cart would do on a treadmill after seeing that popcorn sail past it in natural wind. And remember, he was clever enough to design a cart that had remote steering and could ride the wind without needing a guide wire.
As was the one in the original video by Goodman. Tested and proven as a TM cart, and would have beaten the popcorn handily even if they started at the same time.

It's nice (and still fun!) to run through this without the waters being muddied.
P: 563
 Quote by chingel Thank you for your explanations. Here is where I still have a problem. Doesn't energy matter also? Yes we can use gears to multiply the force, but doesn't the energy stay the same? Eg isn't the energy you put into at one end the same what you get from the other end, no matter what gears you use between? Otherwise you could just connect some gears to a wheel and then connect it to another wheel and multiply the force. You could do that, but doesn't the energy stay the same? To me it seems that it takes a certain amount of energy to make the propeller move the air and that energy can only come from the kinetic energy of the cart, no matter what gears you use. If you use gears to make the propeller slower, the force at the wheels is lower, but since they move more in the same time, don't they expend the same amount of energy as the propeller gets?
Yes, absolutely! That's what we've been talking about the whole time, the fact that the energy input from the wheels is used by the prop, and as such the energy output can never be more than the input. The force output certainly can, just like a lever and that's what we've also been talking about levers.

As mheslep pointed out, when the prop pushes air back relative to the cart it is reducing the speed of the air over the ground (reducing the kinetic energy of the wind) and using that energy to propel the cart (increasing the cart's kinetic energy). Since a real world cart is never 100% efficient, the cart will never reach the theoretical top speed but instead will travel at some percentage of it.

The Blackbird reached 3.5x the wind speed, which is 70% of its theoretical top speed of 5x wind speed; pretty impressive!
HW Helper
P: 6,763
 Quote by chingel Doesn't energy matter also?
This was covered in the previous threads. Note that

power = force x speed

For the wheels, the point of application of force is the ground, which is moving backwards relative to the cart. For the propeller, the point of application of force is the air, which is moving at (ground speed relative to cart) - (wind speed relative to ground) = wind speed relative to cart.

As an example, say the wind speed relative to ground is +10 mph, and that the cart is moving at +25 mph (downwind). Ground speed relative to the cart is -25 mph. Wind speed relative to the cart is -15 mph. If the effective advance ratio is .8, then the propeller would produce thrust at -20 mph relative to the cart if there was no load. This ratio means that with zero losses, the force at the propeller can be 1.25 (25/20) times the opposing force at the wheels. Assume the force at the wheels is 80 lbs, then the propeller could produce up to 100 lbs of thrust with no losses:

power = 80 lbs x 25 mph (wheels) = 100 lbs x 20 mph (propeller)

This results in an ideal net forward force of 20 lbs. The real thrust force and speed will be less, but as long as the net force is greater than rolling resistance and drag the cart accelerates, and in the case of the BB cart, it reaches a max around 3.5x wind speed.

The propeller makes things a bit more complicated than just gearing. The propeller's pitch is part of the effective gearing (and advance ratio). The propeller's size (width and length) affects how much thrust force is produced for a given thrust speed (relative to the air) and pitch. A long (large diameter) propeller will generally be more efficient.

 Related Discussions Advanced Physics Homework 5 Engineering Systems & Design 51 Classical Physics 15 General Physics 175 Aerospace Engineering 11