Hello (RP),
My name is (NASA #2), and (NASA #1) forwarded your email dialog to me, along with some attachments from one of the naysayers of the DWFTTW cart physics. I have been an applied aerodynamics researcher at NASA Ames for 31 years. In addition, I grew up racing sailboats, then after starting work at Ames, left sailboat racing to race sailplanes, also for the last 31 years.
So I am well-acquainted with the performance of sailboats at downwind headings not directly downwind, and it is true that for sailboats, there is a significant benefit to boat speed to do that, primarily from the aerodynamic characteristics of sails. However, that effect is not in play to any appreciable degree on the DWFTTW cart, and if anything, acts to diminish the thrust on the propeller. Drawing the vector diagram of the relative wind (apparent wind) as the sum of the cart speed and the wind speed, it can be seen that if the wind direction swings, the apparent wind increases. If the wind angle approaches 90 degrees, the apparent wind speed will be roughly equal to the ground speed, and the cart will stop. The cart gets its power from the DIFFERENCE between the apparent wind speed and the ground speed, requiring that the apparent wind be LESS than the ground speed.
Interesting that the writer (Humber) in his attempt to make an argument for why the cart can not go DWFTTW, he states exactly why it DOES:
“the prop is said to travel less distance through the air, than the cart travels over the ground, but of course,
work =force*distance, and must be the same at the wheel as at the propeller.”
His statement is true, that for a given interval of time, the work done by the prop must be equal to the work input from the wheels, (excepting for losses). The fact that the prop travels less AIR distance in that time than the wheels travel in GROUND distance is exactly WHY the propeller thrust can be greater than the wheel drag. There are, of course, significant losses in the system, and Mr. Cavallaro’s example problem provides realistic estimates for those, demonstrating that even with those losses, there is excess thrust at the propeller to accelerate the vehicle despite the wheel drag. The only thing that limits the cart speed is the escalation of those losses to the point where there is no longer sufficient power to create the excess thrust. When the thrust equals the drag, the cart will move at constant speed.
On the topic of the small deviations in wind speed and the effect that has — first of all, remember that what is important is the direction of the “apparent wind”. This is also true of sailboats, of course; by sailing at an angle to the wind (reaching angle) the sail performs better as a wing rather than just a drag device. The faster the boat goes, the more the apparent wind swings to reduce the angle of flow onto the sail into the useful range to operate as a wing, providing more ‘lift’ force that has a large component in the direction of motion. Choosing the optimum reaching angle for a sailboat is complex because it involves not only the vector combination of the boat speed and wind speed to find the apparent wind, but also the performance ‘polar’ of the sails – the amount of lift and drag force they produce as a function of angle to the apparent wind. But, for the DWFTTW cart, any reaching angle increases the apparent wind component into the propeller, which reduces its thrust.
One other possibility is worth discussing — that it could be the time-variation of the wind direction, rather than simply the fact that the wind is not DDW. There are examples of similar effects in nature that would give some reason to consider this. For example, what is called “dynamic soaring” -- the maneuvering in a wind gradient field (regions where there is a consistent pattern of different wind speed) that allows birds (and gliders) to soar by extracting energy out of the wind gradient field. This is the life-blood of the albatross, and to some extent, the frigate bird. The world record for a radio-controlled glider in dynamic soaring is something close to 400 mph! In the case of the DWFTTW cart, it might be possible to extract a very slight amount of extra energy from the time variation of the wind – I will at least give it additional thought. But it is certainly not the dominant effect, which is much more simple and, (dare I say...) obvious.
One other observation on the wind data — I am not familiar with the instrumentation used to measure the wind speed in the plots that are presented. The high frequency ( 5hz) oscillations in the wind direction look to me to be partly due to an artifact of the instrumentation. Several possible ways that this would happen occur to me, but each is dependent on assumptions of how the measurements were made, so until I know that, I would not elaborate further on those effects. In any case, they are of very little significance compared to the actually very simple situation of why the cart can go about 3x the wind, down wind.
A quick thought on what additional measurements might be made to help persuade naysayers: Is there sufficient skepticism in the assertion that the propeller is pulling and the wheels are dragging, that some well-placed force measurements might be convincing? Probably the simpler thing would be to build one with electric generator at the wheels and motor at the prop, and show what direction the current is flowing. Even simpler is to just examine the drive chain while it is running, and see which side of the drive gears the chain is tight on. When you pedal a bike, the top leg of the chain is tight -- if the wheel of a bike is forcing the pedals to turn, the bottom leg of the chain is tight. On the DWFTTW cart, this simple test makes it easy to see that the wheels are indeed driving the prop.
It’s funny to me how hard people work to contrive an alternative explanation for something that is actually fairly simple: The propeller thrust is greater than the wheel drag, because the apparent (relative) wind speed is slower than the ground speed. The power (work per unit time) available from drag on the wheels is D x V_g. The power required by the propeller is T x V_a. As long as V_a is less than V_g, then T must be greater than D, ignoring system losses, so that the power absorbed matches the power developed.
I can’t help make an analogy to someone that would argue with Einstein’s proposition that gravity is just the curvature of space-time because they don’t understand it, rather than accept that they don’t understand it and try to fill their knowledge gap.
I respect your efforts to try to reconcile these things, and to try to impose some level of civility into the technical discussion. I often try to do the same. I sometimes find that when the conversation is reduced to simultaneous monologues, it is best to sigh and give up, and until now, I have not spoken out on the DWFTTW. I laud your tenacity.
There are those that get quoted as expressing a certain opinion, and the quote persists long past the time that that opinion is still held. I’m quite certain that if you give me 5 minutes at the chalk board with a Nobel laureate physicist, I can convince him of the validity of the analysis for the DWFTTW cart. I have encountered this before in reverse — someone comes to us with a crackpot idea, and when we naysay it, they site the affirmation of some prize physicist who made a polite and supportive comment during a brief meeting, but who would easily be persuaded later by sound argument that the idea is without merit.
When Mr. Cavallaro is here, I will raise this hypothesis about the effect of small variations in wind direction. I think we can quickly dispel it on his demonstration treadmill by moving the fan in small amounts to one side, and I expect to see the cart slow down.
Best Regards,
(NASA #2).