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Imagine you have wind powered car "Blackbird". The objective is simple make the fastest wind powered car.
So I was watching Veritasium and learned that "Blackbird" can go counterintuitively faster than the windspeed! In fact the claim is at one point it was going $2.8$ times the windspeed (3:12).
Assuming parameters such as mass, etc is there a theoretical upper limit at what percentage of the windspeed such a vehicle can go at?
I expect that the vehicle speed that they attained is very close to the limit for that type of design.
The blackbird vehicle is very flimsy, they are desperately trying to keep the weight down.
The blackbird vehicle is harvesting energy from the difference in velocity between air and ground. That means that it is all about traction.
For going downwind the wheels need to have good traction; when going downwind the wheels are driving the propellor.
A wheel - being in contact with the solid ground - is capable of 100% traction; you just need to make sure the wheel will not slip.
The traction of a propellor, however, is inherently poor, because a propellor is churning air.
Imagine trying to propel an engine driven vehicle with a propellor. For a given engine output a propeller will give you far less propulsion than using the engine to drive the wheels.
For comparison:
In a follow-up video Derek demonstrated a device that I will call 'difference cart'
The difference cart has wheel traction both against the ground and the wooden beam above it.
By making the difference in diameter between the wheels more extreme (or by adding gearing) the difference cart can achieve a higher ratio.
For even more traction you could use toothed belts and gears.
While there are practical limits of course to top speeds (involving propeller supersonic tip speed impacts, etc.) there is no theoretical upper limit to the multiple of windspeed. In other words, achieving say 50x the speed of the wind in a 1mph involves only drive train efficiency questions and not those pesky top speed issues involved if one were attempting 50x in a 20mph wind.
What is the practical limit on multiples? Well, the design point for the hand carved propeller on the Blackbird was 2x the speed of the wind. After construction and success at the design point, a variable pitch hub was installed which extended the design point by a bit. Even with this handicap and cobbled together bike and go-kart parts (and an original budget of $5k), the vehicle has been recorded still accelerating above 3x the speed of the wind (to a 3.3x max as I recall).
That the Blackbird record could be smacked around pretty good given any reasonable budget is a foregone conclusion to those of us in the know. Given a really good budget, multiples of 5-7x should be achievable. Speeds of 140+ could be doable on the top end.
Don't think we haven't thought about it. :)
