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| Mess with your minds: A wind powered craft going faster than a tail wind speed. |
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| IanB:
--- Quote from: electrodacus on December 19, 2021, 05:53:12 pm ---power is instantaneous contains no time dimension --- End quote --- Power is defined as "the rate of doing work" and has dimensions of energy/time. So it certainly does contain a time dimension. |
| IanB:
--- Quote from: electrodacus on December 18, 2021, 10:44:10 pm ---Here are the correct equations for wind power available to a vehicle traveling directly down wind 0.5 * air density * area * (wind speed - vehicle speed)^3 yes this is the correct equation. Notice how you have highest power at low vehicle speed and power drops to zero by the time vehicle speed equals wind speed. --- End quote --- But why is this the correct equation? Please derive this equation step by step from first principles, stating any assumptions made at each step. Then you will understand where and how this equation can be applied, and what limitations exist in its usage. |
| electrodacus:
--- Quote from: Kleinstein on December 19, 2021, 10:58:01 am --- The point is not in reading the euqations, the point is understand what they are actually calculating. The first one is the power theortically available from the wind as the kinetic energy in the moving air. The second equation is giving the energy available at the reduces wind speed, e.g. for a wind-turbine on the moving vehicle. This is not the maximum energy available to the vehicle. The wind turbine also creates some drag force, comparable to a sail and this drag force also creates power to a moving vehicle. This power contribution is force times vehicle speed. For a sail this is the only way it creates power. The wind turbine (=porp) on the vehicle could create some extra power directly. For the sail the drag force is proportional to (wind_speed-vehicle_speed)². For the prop the drag force (called thrust when caused by the driven prop) also depends on the speed the prop rotates. depending on the direction and speed this can be less, but also more than just a sail. With the driven prop there can be drag/thrust even with zero wind speed. --- End quote --- As I said many times before please learn the difference between power and energy. Both equation refer to power only nothing to do with energy. The second equation outputs the ideal case wind power available to any direct down wind vehicle (any means is true for blackbird and for a sail vehicle). The difference is that sail vehicle (an ideal one) takes all this available power and stores it as kinetic energy thus not able to exceed wind speed. Blackbird will split this available wind power in to two. One part will be stored as kinetic energy the other part will be stored as both rotational kinetic energy in the rotating propeller and pressure differential by increasing the difference in pressure between upwind side of the propeller and down wind side. Then this stored pressure differential energy storage is what will allow blackbird to exceed wind speed for some limited amount of time. |
| electrodacus:
--- Quote from: IanB on December 19, 2021, 06:00:58 pm --- But why is this the correct equation? Please derive this equation step by step from first principles, stating any assumptions made at each step. Then you will understand where and how this equation can be applied, and what limitations exist in its usage. --- End quote --- There are multiple resources here is one http://web.mit.edu/wepa/WindPowerFundamentals.A.Kalmikov.2017.pdf The equation can be applied anywhere starting with wind turbine design, power available to any wind powered vehicle, drag power needed for vehicle design ..... |
| IanB:
--- Quote from: electrodacus on December 19, 2021, 06:03:09 pm ---One part will be stored as kinetic energy the other part will be stored as both rotational kinetic energy in the rotating propeller and pressure differential by increasing the difference in pressure between upwind side of the propeller and down wind side. Then this stored pressure differential energy storage is what will allow blackbird to exceed wind speed for some limited amount of time. --- End quote --- But the pressure after the propeller is lower than the pressure in front of the propeller: https://www.quora.com/Why-is-the-static-pressure-before-a-fan-higher-than-after-the-fan I have shown you a video illustrating this. Do you think that video was manipulated or faked in some way? Every engineer knows that video shows the truth. You can do the same experiment yourself. Just use any household fan. You will find the pressure in the moving airstream is lower than the surroundings. You should stop looking at that Wikipedia article. It does not say what you think it says. |
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