GB2374849A

GB2374849A - Aircraft with annular aerofoil

Info

Publication number: GB2374849A
Application number: GB0110471A
Authority: GB
Inventors: Brian Reginald Angel; Peter Laurence Hall
Original assignee: Individual
Current assignee: Individual
Priority date: 2001-04-28
Filing date: 2001-04-28
Publication date: 2002-10-30
Also published as: GB0110471D0

Abstract

An aircraft includes an annular aerofoil over which air may be caused to flow by means of a rotary turbine-like device which rotates about an axis located centrally of the aerofoil to eject air tangentially, or by means of a compressor or other source of air which discharges air to a manifold having outlets through which air is discharged radially. The aerofoil may have a planar downwardly facing surface and a curved upwardly facing surface, and may have a downsweep.

Description

AIRCRAFT Field of the Invention This invention relates to aircraft and is concerned with the provision of an improved form of aircraft which can be regarded as similar to a helicopter, but which does not include a bladed rotor.

Summary of the Invention According to the present invention there is provided an aircraft which includes an annular aerofoil over which air is caused to flow.

The air is preferably arranged to flow over and under the annular aerofoil. The downwardly facing surface of the aerofoil may be planar while the upwardly facing surface thereof is of curvate form. The aerofol may have a downsweep.

The flow of air over the aerofoil may be created by a rotary turbine arranged for rotation about an axis located centrally of the annuls.

The turbine is preferably arranged so that it will eject air substantially tangentially relative to the periphery of the turbine.

The flow of air over the aerofoil may alternatively be created by a compressor or other source of air which supplies air via ducting to a discharge manifold located centrally of the annulus, the discharge manifold having a plurality of outlets through which air is discharged substantially radially of the annuls.

Brief Description of the Drawings Table 1 lists the parameter notation employed herein, Figure 1 comprises vertical and side views of the air flow paths near the annulus, Figure 2 is a triangle for cosine rule calculation to evaluate the angle, Figure 3 is a graph showing the lift calculated for zero downsweep angle and a turbine radius of 7.5 cm. , the lines on the graph (in ascending order) being for DA= 0.5 m. , DA= 1. 0 m. , DA= 2. 0 m., DA= 3. 0 m. and DA= 4. 0 m., Figure 4 is a graph showing the lift as a function of downsweep angle and rotation speed, with the lift calculated for DA = 2.0 m. and RT = 7.5 cm. , the lines on the graph (in ascending order) being for downsweep angles of 0 degrees, 5 degrees, 10 degrees, 15 degrees and 20 degrees,

Figure 5 is a graph showing the lift as a function of downsweep angle and annulus horizontal thickness, with the lift calculated for a turbine rotation speed of 20,000 rpm and a turbine radius of 7.5 cm, the lines on the graph (in ascending order) being for downsweep angles of 0 degrees, 5 degrees, 10 degrees, 15 degrees and 20 degrees, Figure 6 is a graph showing the centrifugal stresses in the turbine for a rotation speed of 20,000 rpm, assuming the turbine material has a density of 5 and that the void fraction is 0.9, the lines on the graph (in ascending order) being for RT values of 0.05m., 0.075 m. , 0.1 m. and 0.125 m. , and Figure 7 is a graph showing the Reynolds Numbers for the air flow calculated for a turbine radius of 7.5 cm. , the lines on the graph (in ascending order) being for DA values of 0.5 m. , 1.0 m. , 2.0 m. , 3. 0 m. and 4. 0 m.

Description of the Preferred Embodiments Reference is first made to Figure 1. Irrespective of the detailed design (e. g. slot arrangements and curvature) of the turbine, when it is spun at relatively high rates, it will eject air approximately tangentially (since the tangential velocity on leaving the turbine, equal approximately to the tangential velocity of the turbine itself, will be much higher than any small radial velocity component). Also, on leaving the turbine, the air will flow in paths which, below and far from the aerofoil, are straight lines (since there

is no longer any acceleration due to the circular motion). (The situation is like a weight being whirled around on a string, which subsequently breaks. The stone flies tangentially.) However, at the top surface of the aerofoil, the streamlines will become circular arcs following the surface. For laminar flow, the velocity of these streamlines will exceed that of the streamlines at the lower surface because of the longer distance around the arc.

For the linear streamlines on the underside of the aerofoil :

Figure 1A shows a typical air-path path over/under the aerofoil (AC). The direction of flow is not quite radial since the edge of the turbine does not correspond to the axis of the system. However, if Rr < < Ro, the error in neglecting this deviation should be negligible.

The calculations set out below have, therefore, been based on the assumption that the air-flow is exactly radial in a direction like OC.

Figure 1B is a horizontally projected view for calculation purposes of the paths of air from D to C.

The linear distance DC is given by

The longer distance DC along the arc is given by

where p is in radians. Applying the cosine rule to the triangle DCE (Figure 2) gives:

which gives

By rearrangement, we obtain

so that

from which it follows that the air velocity at the curved surface of the annulus will be given by

By Bernoulli's equation, and neglecting the small pressure changes due to the difference in heights between the top and bottom surfaces, it can be shown that for a zero downsweep angle the differential pressure between the bottom and top faces will be given by

In the general case where the downsweep angle is non-zero, there is an additional term in the lift which is proportional to the rate of change of vertical momentum across the aerofoil. The vertical

IN IV veiocity changes between D and C, increasing from zero to U2 Sine, giving an expression for the effective differential pressure of

Substituting the values for the velocities, and integrating over the area of the base of the annulus (in this case, just a simple multiplication), it can be shown that the lift force is given by

It should be noticed at this point that the maximum height h of the annulus has not been introduced into this equation, although it must be a design consideration, since presumably to ensure good laminar flow above and below the aerofoil it is required that the height of the turbine H is at least greater than the maximum annular height h. However, h is not really an independent parameter, since it can be derived from Ro, R, and Rc using a theorem relating the subdivisions of a chord and a diameter of a circle :

from which it may be shown that h is given by

In the calculations which follow, there is assumed a ratio:

which implies that the angle p is approximately 39 degrees, and also that

which seems reasonable, but is probably not optimal.

It is difficult to calculate what minimum air-flow is necessary, or the effect of changing the momentum of air which is sucked into the turbine. It has been assumed (without proof) that the mass airflow is not critical, as long as the turbine is tall enough to achieve a reasonably laminar flow over both the lower and upper surfaces of the annuls. Likewise, it is assumed that this mass, and the velocities involved, are not large enough for the rate of change of air momentum within the turbine itself to significantly affect the lift.

Even if this were non-negligible, the options exist to have the open pipe at the axis of the turbine to point upwards or downwards.

(Pointing downwards is better, as sucking air upwards and then turning it in a horizontal direction would tend to give a positive contribution to the lift proportional to the rate of reduction of upward momentum.) From standard theory, the nature of the flow will be characterised by a Reynolds number given by

Finally, it is possible to attempt to calculate a notional stress in the turbine material arising from the centrifugal forces when it is spun at a high rate. The actual stresses will depend on the detailed design of the turbine, and could be simulated by finite element methods, e. g. in a modem CAD package. A notional stress is

assumed, given approximately by the centrifugal force per unit area of the curved surface:

where the mass of the turbine is given by

and the curved surface area is

from which we obtain

Figure 3 shows the lift (in metric tonnes) as a function of the turbine rotation speed for a value of e = 0. Data are calculated for a range of values of the horizontal size of the annuls. At this flat angle, it requires both a high rotation speed ( > 20,000 rpm) and a fairly large horizontal thickness (difference in outer and inner radius) of the annular disk of ca. 3 metres or more to get any useful payloads, e. g. a few metric tonnes. The situation is much improved by creating a downsweep angle from the inside to the outside of the annuls.

Figure 4 shows the lift calculated for a value of DA of 2 metres and a turbine radius of 7.5 cm for a range of values of the rotation speed, while Figure 5 shows similar plots as a function of annular disk size ranging from 0.5 to 4 metres for a rotation speed of n =20,000 rpm, at the same turbine radius. The different plots in both figures are for values of e ranging from 0 to 20 degrees. It can be seen that even a modest downsweep angle significantly enhances

the lift of the system, enabling either the rotation speed or the annular size to be reduced proportionately.

Another way of increasing the lift for a constant rotational speed is to increase the radius of the turbine. However, an increase in either turbine radius or rotation speed will adversely effect the centrifugal stresses in the turbine material.

Figure 6 illustrates a notional calculation of these stresses as a function of turbine radius and rotation speed. These calculations were made for DA=2 metres, pi= 5 x 103 kg/m3 and < 1 > =0. 9 (i. e. 10% of the turbine is solid). The stresses range up to a few hundred bars. The turbine accordingly should preferably be a single casting or moulding from a strong and relatively low density material.

Finally, Figure 7 shows the Reynolds Numbers of the flows, calculated for a range of annulus sizes and rotation speeds, assuming a turbine radius of 7.5 cm and the density and coefficient of viscosity of air as being 1.3 kg/m3 and 1.78 x 10-5 Pa s respectively (Francis, 1969). The values of Re range from about 106 to 7 x 107, in all cases well beyond the critical Reynolds Number for the onset of turbulence (ca. 5 x 105). This suggests that eddy turbulence will occur at the outer edges of the annuls. However, it may have less impact on the lift characteristics of the system than it might have on any superimposed lateral (forward) drive.

A relatively large disk seems to be required (typically 3 metres differential radius, e. g. an outer radius of 3.2 metres and an inner

radius of 0.2 metres), pius a relatively iarge rotational speed of around 20,000 rpm or greater.

The turbine should preferably be made from a single casting or moulding of a relatively light and strong material.

The lift characteristics can be improved by introducing a downsweep angle (angle of attack); or by increasing the diameter of the annulus, the diameter of the turbine or the rotation speed.

The direction in which air is sucked into the turbine may not be significant, but sucking air upwards would be better than sucking it downwards.

The air flow falls into the turbulent regime, and there is likely to be eddy or vortex circulation at the edge of the annuls. The impact of this on any horizontal drive might be greater than the effect on the lift characteristics of the system.

In an experiment carried out to verify the theoretical

calculations, a model has been produced in which :Ro = 0. 31m., R, = 0. 0975 m., RT = 0. 09 m., e = 180, and rate of rotation of turbine = 3, 000 r. p. m.

The model produced a measured lift of at least 2 Kg. as compared with a theoretical lift of 2.2 Kg. at 2,700 r. p. m.

As an alternative to using a turbine to generate the flow of air over the aerofoil, it is possible to generate a high velocity flow of air by means of a compressor, engine or the like and to direct the high velocity flow of air under pressure via ducting to a manifold which is located at the centre of the annular aerofoil and which has a plurality of angularly spaced radial outlets through which the high velocity flow of air exits to flow under and over the aerofoil and to obtain results such as those which have been outlined above with a turbine.

The aircraft of the present invention has a number of advantages as compared to helicopters, for example, there are safety benefits as a result of the very considerable reduction in the number of moving parts, and there are environmental benefits as a result of the substantial reduction in the amount of noise which is generated.

Claims

Claims :-

1. An aircraft which includes an annular aerofoil over which air is caused to flow.

2. An aircraft as claimed in Claim 1, in which the air is preferably arranged to flow over and under the annular aerofoil.

3. An aircraft as claimed in Claim 1 or Claim 2, in which the downwardly facing surface of the aerofoil is substantially planar while the upwardly facing surface thereof is of curvate form.

4. An aircraft as claimed in Claim 1 or Claim 2, in which the aerofoil has a downsweep.

5. An aircraft as claimed in any one of the preceding claims, in which the flow of air over the aerofoil is created by a rotary turbine arranged for rotation about an axis located centrally of the annuls.

6. An aircraft as claimed in Claim 5, in which the turbine is arranged so that it will eject air substantially tangentially relative to the periphery of the turbine.

7. An aircraft as claimed in any one of Claims 1 to 4, in which the flow of air over the aerofoil is created by a compressor or other

source of air which supplies air via ducting to a discharge manifold located centrally of the annular aerofoil.

8. An aircraft as claimed in Claim 7, in which the discharge manifold has a plurality of outlets through which air is discharged substantially radially of the annuls.

9. An aircraft having a lift-generating annular aerofoil substantially as hereinbefore described.

10. A method of generating lift substantially as hereinbefore described.