All you need to convince me is provide an equation describing the available wind power to Blackbird.
Pw = (0.5 * air density * area * (wind speed - vehicle speed + wash speed)3) - Pp
where:
wash speed = velocity of air being pushed back by the propeller
Pp = power required to turn the propeller
Any equation that ignores the propeller (which is a pretty big part of the entire thing, you know!) is obviously missing something and not appropriate.
The question that I asked was Wind power available to vehicle as vehicle is powered by wind power only.
The propeller itself is powered by wind so whatever contribution the propeller makes can not be added to wind power as it is already powered by the wind.
I did not asked about the Power available to vehicle to accelerate as that is not just wind power but after vehicle starts to move is wind power + power provided by the energy storage.
If you want to think vehicle has no energy storage available then it will be nothing other than wind power available and so vehicle could not exceed wind speed.
Take the first fraction of a second for example when vehicle is stationary and will just start to move
Wind speed = 6m/s
vehicle weight = 10kg
area = 1m^2
P
w = 0.5 * air density * area * (wind speed - vehicle speed)
3Say this wind power is split this way (the way it is split will depend on your wheel to propeller gear selection and propeller pitch angle and propeller design)
50% will be used to accelerate the vehicle and 50% used to power the propeller and say proeller is 65% efficient.
Say the integration time interval for this finite analysis calculation is 1 millisecond = 0.001 seconds
Then in this initial first step
P
W = 0.5 * 1.2 * 1 * (6-0)
3 = 129.6W
But only 50% of this will be used to accelerate the vehicle so 64.8W and so after this first 1ms the vehicle has gained 64.8mWs = 64.8mJ
Then the other 60% at 65% efficiency will be 129.6W * 0.5 * 0.65 = 42.12W net at propeller
You consider this stored energy and add in next step to the Potential wind energy so currently potential wind energy is
(0.5 * mass * w
2) - (0.5 * mass * v
2) = 0.5 * 10 * 6
2 = 180Ws
So a sail only vehicle will accelerate faster as it will not need to provide 50% of wind power to propeller but the Potential wind energy will drop as vehicle accelerates
On the Blackbird significant part of wind power is diverted to propeller and that pushes back creating higher pressure (sort of like increasing equivalent wind speed relative to vehicle) and so potential wind energy will decrease much slower in the initial acceleration part where there is a lot of wind power available.
In my video I use vehicle speed steps of 0.01m/s instead of time for better resolution with less steps.
In any case the main point is that vehicle (any wind powered vehicle) has just the wind power provide by the formula I mentioned and in the special case of the Blackbird part of the energy is used to power the propeller with the remaining accelerating the vehicle.
If there was no energy storage like for example air was not compressible then all the power you diverted to propeller will immediately push the vehicle.
So say vehicle was traveling through water (non compressible fluid) instead of trough air.
Then out of "Wind" power available half will accelerate the vehicle and the other half go to propeller and say propeller was 100% efficient that will also push the vehicle with the other half so total 100% of available power will accelerate the vehicle but nothing is stored.
With air which is compressible (elastic type of storage like a spring or repulsion forces between electrons) when you send half the power to propeller and say again 100% efficient propeller you get less than that half in push power as air compresses and some of the energy is stored in pressure differential instead of as vehicle kinetic energy keeping the vehicle a longer time at lower speed and so give it a chance to store energy in that pressure differential.
As vehicle picks up speed more and more of the acceleration is contributed from the stored pressure differential and less provided by the wind.
That is how the treadmill vehicle can drive against the motion of the treadmill surface because while you keep the vehicle in place the propeller builds up pressure differential (low pressure in front and high pressure in the back) and so when you let go that pressure differential is what pulls and pushes the vehicle forward and all energy that is not needed for acceleration and friction is put back by the propeller.
That treadmill vehicle is a much better experimental case as everything is much more controllable (fairly constant treadmill speed) and zero wind speed as it is indoor.
With any high speed camera even 60 or 120FPS you can see when video from the side that vehicle acceleration rate decreases meaning it will get to a point where it will stop accelerating and you can fairly precisely calculate what that time will be and you can also calculate the total stored energy if you know vehicle weight and friction losses.