discussed the rotation a birds wing undergoes at the end of its

stroke.

The description was of the vortices this produces and how this

contributes to lift. No doubt this does occur, but I was reminded of

the way that a swimmer rotates his hand on the return stroke while his

hand is still in the water so as not to counteract the thrust he

already produced.

I thought then this same idea could be used to produce craft capable

of hovering, as helicopters do. You would have a cupped surface moved

vertically downward producing a downward thrust, but on the return

stroke the surface would be collapsed so as not to counteract the

thrust already produced. I'll refer to the cupped surface as a canopy

whether of not it is stiff during the propulsion phase or flexible as

an actual parachute.

I'll use the formula for drag to calculate the thrust that would be

produced:

Drag (physics)

formatting link

It is the drag is 1/2 times the density, times a reference area,

times the drag coefficient, times the velocity squared. Note that

usually the reference area in this formula would be the cross-

sectional area, as for instance for an airfoil. However, for a

parachute the reference area that goes in this formula is the surface

area.

The power required to overcome drag is also given on this page as the

velocity times the drag. From this we see the ratio of thrust to power

required is 1/v, where v is the velocity. This means it would be more

efficient to move the canopy at lower velocities.

For thrust given in terms of newtons, and power in watts, this thrust

to power ratio would be in newtons per watt. This lifting capability

for the power required is sometimes given in terms of kilos lifted to

kilowatts of power or grams per watt. For this scenario and for the

velocity given in meters/sec, the numerical value of grams to watt

power would be about 100/v.

The efficiency of helicopters is in the range of perhaps 10 grams

lifted per watt. Then this proposed method would exceed the efficiency

of helicopters if the downward velocity of the canopies was less than

10 m/s, 36 km/hour.

If we made the downward velocity say 5 m/s the efficiency would be 20

gram/watt. Say we wanted to make a personal hovering device capable of

lifting a person. Let's suppose the total weight was 200 kg, including

the person, engine, canopies, support structure etc. Then we would

have to have the thrust be at least 2000 newtons. The density of air

at sea level is 1.22 kg/m^3. For a parachute, the drag coefficient Cd

is perhaps 1.5 to 2. The surface area of a hemispherical canopy is

2

***Pi***radius^2. This would result in a radius for the canopy of about

3.2 meters or a diameter of 6.4 m. You could of course break the

surface area up into more than one canopy. Note that to reduce the

volume of the craft, it may also work to have several of the canopies

in a single column.

For an efficiency of 20 gram/watt and lifting capability 200 kg this

would require a power of 10,000 watts, about 13 horsepower, quite low

for a power plant capable of lifting a person.

I originally was thinking of this for heavy lift applications

however. A common heavy lift helicopter is the S-64 Skycrane. It can

lift a gross weight of 20,000 kg using 7,000 kwatts of power with a 22

meter diameter rotor. This is actually a weight to power ratio of only

3 to 1.

Suppose we wanted to get a 5 to 1 ratio using the same power. This

would require a velocity of 20 m/s in our scenario and a lifting

capability of 35,000 kg, or a thrust of 350,000 N. Then to get the

350,000 N thrust would require diameter of about the same size as the

helicopter rotor. But this would be able to lift almost twice as much.

To allow further lift during forward flight and reduce the forward

drag we may make the canopies in the shape of parafoils. Note that

parafoils create most of the reduction in descent speed from the fact

they produce lift, with a relatively small amount coming from the drag

they produce. Then it might be advantageous to use these moving in a

horizontal direction to generate the hovering effect. We might also

want to change the shape of the canopies depending on the direction of

flight, vertical, horizontal or a combination.

The idea might be usable for supersonic or hypersonic propulsion as

well. In this instance the canopies would not have to be moving at

supersonic velocity with respect to the surrounding air. Their

velocities would be at or a little more than that at which the ambient

air is moving rearward (with respect to the craft) in order to get the

highest efficiency.

Bob Clark