# Design Of A Propeller For Downwind Faster Than The Wind Vehicle

#### kolibri282

##### Super Member
title: Design Of A Propeller For Downwind Faster Than The Wind Vehicle
author: Shethal Thomas Kodiyattu
comment: this paper mentions the design of a propeller driven vehicle that can go downwind faster than the wind dating back to 1960

PS: The report was added to the data base because of this thread:

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#### Jean Claude

##### Junior Member
It seems to me that the possibility of this faster-than-wind machine is easily explained, without the need for a wind gradient or a momentary lull. Here is why:
1) If a power Pshaft is taken from the axle of the wheels travelling at a speed Vgnd relative to the ground, this produces a rolling drag such that
Pshaft = D . Vgnd (neglecting the friction losses)

2) If we apply a power Pshaft to the shaft of a propeller, it creates a traction TProp in the air where it moves such that
Pshaft = TProp.(Vair + Vi)
(neglecting the friction losses)

3) If the power applied to the propeller shaft is that taken from the wheel axle, then :
Tprop.(Vair + Vi) = D . Vgnd
And if the wind Vwind relative to the ground is in the direction of travel of the vehicle, then
Vair = Vgnd - Vwind

Hence Tprop . (Vgnd - Vwind + Vi) = D . Vgnd or Tprop / D = Vgnd /(Vgnd - Vwind + Vi)

So, Despite the fact that the speed is already higher than the wind speed, the acceleration is still possible if Tprop >D , i.e. when
Vgnd / (Vgnd - Vwind + Vi) > 1

It is the case when, for example, Vgnd is 10 m/s, V wind is 5 m/s, Vi is 2 m/s giving Vgnd / (Vgnd - Vwind + Vi) = 1.43

PS: ERROR: The air stream contracts as the propeller passes. Drawings corrected.

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#### Jean Claude

##### Junior Member
It may seem incredible that this machine still accelerates easily when its speed equals that of the wind, its propeller no longer being bathed in any relative wind.
It is just that it is not like a wind turbine that mechanically drives the rotation of the wheels. On the contrary, it is the rotation of the wheels that mechanically drives the rotation of its propeller.
But let's be careful not to see this as a kind of perpetual motion: The difference between the ground speed of the wheels and the air speed of the propeller creates the positive energy balance capable of overcoming the frictions, by a drop in the ground speed of the air mass after the vehicle has passed.
Here is a spreadsheet taking into account the various energy losses.

Top table: walking with the wind
Bottom table: Walking against the wind

Yellow boxes: Data
Blue Boxes: Results
Other: Intermediate calculations

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