1. A propulsion system for a body, which derives momentum from expelled mass, the system including an engine being mounted to the body to enable it to execute a peripheral trajectory relative to the body substantially about a centre of motion, wherein the engine is mounted so that, when operational, it expels mass in an inward direction with respect to the trajectory.
2. A system according to claim 1 further comprising a motor adapted to rotate the engine along the peripheral trajectory
3. A system according to claim 1 wherein the trajectory is circular.
4. A system according to claim 1 wherein the trajectory is elliptical
5. A system according to claim 1 further comprising a solar panel to provide power for the motor.
6. A system according to claim 1 wherein the engine is mounted relative to the body on platform, adapted to provide motion of the engine relative to the body along the peripheral trajectory.
7. A system according to claim 6, wherein two engines are mounted on the platform, at opposing locations about the centre of motion.
8. A system according to claim 6 having a pair of platforms, mounted to execute oppositely-directed peripheral trajectories.
9. A system according to claim 1 wherein the engine is oriented to expel mass in a substantially radial, inward direction with respect to the trajectory and its centre.
10. A method of generating momentum in a body having an engine which converts stored energy into kinetic energy, the method comprising the steps of: moving the engine along a peripheral trajectory with respect to the body and substantially about a centre of motion;
while moving along the peripheral trajectory, expelling mass from the engine in a direction of expulsion which is inward of the trajectory and, thereby, applying an impulse to the body in a direction opposite to a direction of expulsion.
11. A method according to claim 10 wherein the engine is moved along a substantially circular trajectory.
12. A method according to claim 10 further comprising the step of moving a further engine along the trajectory, both engines moving along the trajectory in opposite directions and at substantially the same rate.
13. A method according to claim 12 wherein the trajectory is substantially circular, and both engines are oriented to expel mass in a direction which is substantially radially inward with respect to the centre of motion.
14. A method according to claim 10 wherein the trajectory is substantially circular.
15. A method according to claim 10 further comprising the step of operating a motor, independent of the engine, to move the engine along the trajectory.
16. A method according to claim 15 further comprising the step of powering the motor from one or more solar panels.
17. A method according to claim 10 wherein the engine is oriented to expel mass in a radial, inward direction with respect to the centre of motion.
18. A method according to claim 10, applied to adjust the orbit of a satellite.
BACKGROUND TO THE INVENTION
1. FIELD OF THE INVENTION
The present invention relates to engines, including but not limited to engines for traction or propulsion, jet and rocket engines, internal and external combustion engines and, indeed, any engine that operates by deriving, in some way, momentum from the conversion of stored energy into another form, such as kinetic. Examples of stored energy include mechanical potential energy and chemical energy.
2. DESCRIPTION OF RELATED ART
One example of such an engine is a simple rocket engine. A chemical reaction within the rocket results in the ejection, from the rocket, of mass in the form of burnt fuel. The impulse applied to the rocket by its engine over any given period of time by the ejection of fuel is equal to the resulting change in momentum of the rocket, as expressed by the equation:
Ft = In(V 1 - V 2 )
Where: F is the force applied to the rocket by the fuel t is the time interval over which the force F is applied m is the mass of the rocket
V 1 is the velocity of the rocket prior to burning the fuel V 2 is the velocity of the rocket after burning the fuel
Assuming, for the sake of simplicity, a constant mass (i.e. ignoring the loss of mass resulting from ejection of burnt fuel) the increase in momentum of the rocket is therefore equal to the increase in momentum of the ejected fuel as a result of the chemical reaction which gave rise to it, the momentum of the ejected fuel being the product of its mass and its velocity upon ejection. The efficiency of rocket fuel can be characterised as its ability to convert chemical energy into momentum. Since, conventionally speaking, the mass of fuel loaded onto any given rocket is fixed, the efficiency of that fuel is measured entirely by how much chemical energy is stored in a given fuel mass. Higher levels of chemical energy in a fuel result in more kinetic energy when that fuel is burnt, meaning that the ejected fuel has a higher ejection velocity which, in turn, means greater momentum for the same mass of fuel.
Conventionally speaking, therefore, there are only two ways in which to increase the capacity of a rocket engine. Firstly, an engine can carry a greater mass of fuel, thereby to enable it to derive momentum from the conversion of the stored chemical energy into kinetic energy and consequent ejection of fuel mass over a longer period of time, since there is more mass to eject at the same ejection velocity. Secondly, the chemical energy stored within a given mass of fuel can be increased, which has the effect of increasing the kinetic energy which results from the burning of a given fuel mass and, thereby, the ejection velocity, meaning the same momentum can be derived from a smaller mass of fuel. The former solution is, to some degree, self- defeating since the more fuel that is carried, the greater the mass of the rocket meaning, in turn that more fuel is required to power it. This places a practical limit on the mass of fuel that can be carried. The latter solution also has practical limits in that rocket fuels must be chemically stable until burnt, whereas greater stored chemical energy usually equates to a greater instability and, therefore, a greater risk. It should be appreciated that, while the conundrum set out above has been exemplified with reference to a canonical example of a simple rocket engine, it is applicable to any engine which harnesses momentum from stored energy. An internal combustion engine of a car is such an engine.
SUMMARY OF THE INVENTION
Embodiments of the present invention provide a manner of increasing the efficiency or capacity of an engine which operates by expelling fuel to produce an impulse upon a body.
According to an embodiment of the present invention there is provided a propulsion system comprising an engine having a vessel from which, in operation, a fuel mass is expelled, thereby to cause a reaction upon the vessel which is equal and opposite to the impulse provided by the momentum of the expelled fuel mass, wherein the engine vessel is mounted to enable it to travel in a circular trajectory and the fuel mass is expelled from the vessel in an inward direction with respect to the circular trajectory.
A further embodiment of the present invention provides a propulsion system including an engine which generates locomotive momentum from expelled mass, the engine being mounted to execute a peripheral trajectory substantially about a centre of motion and the system further comprising a motor adapted to rotate the engine
along the peripheral trajectory, wherein the engine is mounted so that, when operational, it expels mass in an inward direction with respect to the trajectory.
Yet a further embodiment of the present invention provides a method of generating momentum in a body having an engine which converts stored energy into kinetic energy, the method comprising the steps of: moving the engine along a peripheral path with respect to the body and substantially about a centre of motion; while moving along the peripheral path, expelling mass from the engine in a direction of expulsion which is inward of the peripheral path and, thereby, applying an impulse to the body in a direction opposite to a direction of expulsion.
Yet a further embodiment of the present invention provides a method of adjusting the trajectory of a satellite comprising the steps of: powering a motor mounted on the satellite from solar power; using the powered motor to move an engine, which is mounted to the satellite, along a peripheral path substantially about a centre of motion relative to the satellite; and while the engine is moving along the peripheral path, expelling mass from the engine in a direction inward of the peripheral path, thereby to apply trajectory-adjusting force to the satellite in a direction opposite to the direction of expulsion.
In one modification of one or more of the above embodiments, the peripheral path may be circular, though this is not essential. Embodiments may provide for alternative geometries of peripheral trajectory such as, for example, an elliptical trajectory, which may provide advantages, and particularly if energy can be efficiently stored as potential energy in some phases of the trajectory and converted to kinetic energy in other phases without substantial losses.
According to a further modification of the above embodiments, two or more engines are mounted on a body adapted to execute the peripheral path, so as to balance the masses. In yet a further modification, counter-rotating bodies are used, to reduce what might be described as gyroscopic effects, i.e. the effect of the angular momentum of a rotating body.
Typically, where the engine is a combustion engine of some description, the expelled mass may be burnt fuel. Where such an engine is used, one modification provides a fuel store which is stationary with respect to the rotating engine, thereby to reduce the mass which is rotated and, therefore, the energy required to produce that
rotation. In such an embodiment, a sufficient amount of fuel is loaded from the stationary store into the engine and the engine is rotated with that fuel mass.
The system of the present embodiment will preferably include a motor, independent of the engine, which is operable to rotate the engine in the circular trajectory.
BRIEF DESCRIPTION OF DRAWINGS
Embodiments of the invention will now be described, by way of example, and with reference to the accompanying drawings, in which:
Figure 1 is a diagrammatic illustration of an experimental set-up;
Figure 2 is a diagrammatic illustration of an explanation modelling an effect observed according to the set-up of Fig. 1 ;
Figure 3 is a diagrammatic illustration of an earth satellite comprising an engine according to an embodiment of the present invention; and
Figure 4 shows an alternative trajectory for an engine in an embodiment of the present invention.
DESCRIPTION OF PREFERRED EMBODIMENTS
The drawings illustrate both the effect underlying the present invention as well as the experimental setup which evidences the existence of this effect. In the experimental set-up of Figure 1 , the 'engine' is mounted upon an arrangement that enables it to travel on a peripheral path about some notional centre of motion. In the present embodiment the engine is mounted on a rotating platform, provided by a horizontal wheel 11 that can rotate on a vertical axle 12. The rotating platform is suspended on a wire. Accordingly, in the illustrated embodiment, the path is substantially circular, though this is not essential. At the periphery of the wheel 11 is located a cylindrical cup 13 containing a compression spring 14 and a spherical mass 15. The spring is latched in compressed condition by a latch 16. A like arrangement, not shown, is located opposite to balance the wheel. The cup 13 is directed inwardly of the trajectory which it travels along as a result of being mounted to the wheel 11 and, in the present example, is aimed away from the axle 12, though this is not essential. With the wheel 11 stationary, the latch 16 is released - this can be done by radio control - and the spring 14 pushes the mass 15 out of the cup 13.
Clearly, the wheel 11 will recoil. The axle 12 will swing on its wire suspension in a direction opposite to the departing mass 15. The wheel will also acquire angular momentum from the component of force parallel to the tangent at the location of the cup 13. To measure the deflection, a laser pointer, not shown, is attached to the axle beneath the wheel, pointing to a target on the ground. The displacement of the wheel is therefore indicated by the laser pointer.
Now, the cup 13 is reloaded, and the wheel 11 is centred and set in rotation on its axle 12, as shown by the arrow. The latch 16 is released, and the mass 15 ejected by the spring 14. Again, the wheel 11 will recoil. Surprisingly, with the wheel now rotating, its displacement, as indicated by the laser pointer, is greater than when it is stationary. Experiments indicate that the faster the wheel rotates, the greater is the displacement, up to a limiting rate of rotation, beyond which. the spring is unable to eject the ball from the cup.
The significance of this observed effect is that, for a system which has no greater mass, greater momentum can be obtained. It would, therefore, be possible to apply this effect for use in a system which has a finite mass from which to derive locomotive momentum such as, for example, a rocket engine in an orbiting satellite, used to adjust its orbiting trajectory, in which the expelled fuel would be analogous to the moving ball 15.
A simplified model of the effect observed in the experiments described above will now be described with reference to Fig. 2. Further modelling and exposition is provided in the Technical Annex appended to this specification. Referring now to Fig. 2, the ball 15 is illustrated in two positions. Position P 1 is the position at which the catch is released and the spring 14 starts to act upon the ball 15 to eject it from the cup 13; at position P 1 , therefore, the ball 15 starts to move independently of the cup. Position P 2 is the position at which the spring 14 ceases to act on the ball, in other words the position at which the ball 15 has been entirely ejected from the cup 13. For the sake of geometric simplicity, in the modelled example of Fig. 2, the cup 13 is aligned so that its axis intersects with the rotation of the axis of the wheel 11. In the course of travelling along the arc between the positions P 1 and P 2 the ball 15 is, as a result of the release of the catch and, consequent upon that, the force applied to it by the spring 15 in ejecting it from the cup 13 and causing it to move relative to the cup 13 (and, therefore, the rim of the wheel), no longer constrained to move with the
cup along the trajectory of the rim of the bicycle wheel. At the point P 2 of complete ejection from the cup 13, the ball 15 will, in the course of its motion relative to the cup as a result of the force applied by the spring, also have translated along the Y axis by an amount δy as a result of its continued movement with the cup. The ball 15 will therefore, at this point, have a velocity along the Y axis which is attributable solely to its motion with the wheel of:
where δt is the time taken for the wheel to rotate through the arc between positions P 1 and P 2 .
The momentum M of the ball 15 along the Y axis is the momentum the ball 15 acquires as a result of its continued movement within the cup, along an arc of a circle defined by the bicycle rim, during the time interval δt in which it is ejected. In other words, the momentum M is the additional momentum the ball acquires as a result of its circular trajectory, in comparison with the momentum when remaining stationary while the spring 14 ejects the ball 15 from the cup 15. This additional momentum M is given by the expression:
m δy/ δt
where m is the mass of the ball.
To reiterate, the momentum M is the additional momentum of the ball as a result of rotation of the wheel which, in a freely-suspended wheel, causes the experimentally- observed increased deflection of the wheel when rotating during ejection of the ball from the cup, and manifesting itself as an increased deflection of the wheel produced by an increased reaction force due to this increased ball momentum.
Where the ejected mass is burnt fuel from a rocket engine, a key parameter is the period of time δt during which the thrusters are operating. Accordingly, it would be useful to be able to express this additional momentum provided by rotation of the engine in terms of this time period, together with geometric parameters as well as other measurable parameters of operation such as the speed of rotation.
From characteristic geometries of triangles:
θ + φ = 90
φ + 2α = 180
φ = 2θ
For small values of δt and, therefore, small values of δr, the chord δr will approximate to the arc travelled by the ball 15 between positions P 1 and P 2 during the time period δt.
From basic trigonometry:
δy/ δr = sin θ
For small angles, in radians:
sin θ ~ θ ~ δy/ δr
substituting for δy and θ:
M = m (φδr/2δt)
From simple circle geometry:
φ/2π = δt/T φ = 2π δt/T
(where T is the time period for a complete revolution) and
δr/2πR = δt/T δr = 2πRδt/T
where R is the radius of the wheel, substituting for φ and δr:
M = m [2π/T] 2 R δt
where R is the radius of the circular path which the engine rotates upon, and T is the time period for a single revolution of that path.
Thus, the longer the spring 14 takes to eject the ball 15 from the cup, the longer δt and the larger additional moment which the ball 15 will acquire as a result of its rotation during the course of its ejection. Similarly, the faster the wheel rotates, the smaller the value of T and the larger M is.
Both of these observations, however, have limits. Firstly, it is observed, consistent with the theory expressed above, that the faster the speed of rotation, the greater the additional momentum acquired by the ball. This applies, however, up to a limit above which the spring 14 is unable to apply sufficient force to overcome the reaction force applied to it and arising as a result of the linear acceleration of the ball 15 and cup 13 along the Y axis during the course of executing circular motion. Above that limit, therefore, the spring 14 is unable to eject the ball 15 from the cup. Secondly, it should be noted that the above expression is derived with reference to approximations: that the arc travelled during the time for ejection is small enough to be approximately linear; and that, relatedly, the angles are small.
The applicability of this principle to a satellite will now be explained by reference to a thought experiment. Consider two rockets, each containing a satellite. Both rockets contain identical satellites, each having their thruster engines - by which is meant those engines which are used to adjust its trajectory once in orbit - mounted upon a wheel. The first satellite is launched with the wheel stationary; the second satellite, prior to launch, has the wheel spun up to a high angular velocity. The mass of both satellites is identical. However, once in orbit, the thrusters of the second satellite, which are mounted on the rotating wheel, will be able to generate more locomotive momentum from burning the same mass of identical fuel than the thrusters of the first satellite, whose thrusters are mounted the stationary wheel. The thrusters of the second satellite can therefore generate the same locomotive momentum from burning a smaller mass of fuel, thereby enabling the second satellite to remain in orbit for longer - even though only the same mass has been carried from earth.
Even at an entirely theoretical level, the limitations of this thought experiment can be readily appreciated. Firstly, the satellite with the stationary wheel has no use for the wheel, and so could, instead, carry an additional mass of fuel to be burnt and used in the conventional manner. Any efficiency gains as a result of rotation would, therefore, have to be sufficiently large to exceed the penalty of carrying the mechanism which provides rotation of the thruster in order to be significant. Secondly, the rotating wheel would have significant angular momentum which would constitute a penalty when launching and piloting the satellite to the appropriate orbiting trajectory. While both of these limiting factors are real, it is believed that both can be overcome so that this effect can be efficiently employed, for example in a satellite.
An example is shown with reference to Figure 3. Referring now to Fig. 3, a satellite has a payload section 22 and solar panels 23, an engine compartment comprising a fuel tank 24 and platform providing a peripheral trajectory for the engine 24, here provided by a rotating wheel 26. The wheel carries engines, here provided by oppositely-disposed thrusters 27, 28. Thruster 28 is shown in the fuelling position, in which fuel from tank 24 is admitted via a fuel line 29. The thruster 27 is shown in the firing position, in which its fuel, acquired from the tank - which is stationary with respect to the rotating thruster (to reduce the mass which must be rotated) is fired by a control arrangement 25. The platform is powered by a motor 30.
Because of the effect demonstrated in the experimental set-up of Figure 1 , to which this thruster set-up is mechanically equivalent, the locomotive momentum generated by the thruster, and thereby the reaction of the expanding fuel against the closed end of the thruster 27 will be greater than if the thruster were simply mounted, without a rotating carrier, in the satellite. Thus, to achieve a given change in velocity of the satellite 21 , less fuel is needed. Either less fuel can be loaded , for a given mission, increasing payload capacity, or a given fuel load can have an extended life, usefully extending the life of the satellite 21.
Figure 3 illustrates a satellite with just one thruster. In practice, more than one thruster is provided, to effect adjustments in orientation, perhaps in order to keep an antenna aimed at an earth location, or the solar panels deployed for maximum insulation. The principle is applicable to other types of engine that depend on the reaction of a fluid such as an expanding gas, as will be generated by burning fuel,
against a reaction surface. As will be readily appreciated, engines mounted on any given rotating platform are only capable of applying an impulse in the plane of rotation of the platform to which they are mounted. Thus, as many rotating platforms will be required as directions of desired impulse in order to provide the requisite orbit correction adjustment.
Whether a wheel or other rotating platform for mounting of a satellite is spun prior to launch or afterwards, in practice two counter-rotating wheels may be provided, each carrying thrusters. This has a number of beneficial effects. Firstly, the angular momentum of the thruster rotation, and therefore the gyroscopic effect of a rotating object upon the trajectory is substantially nullified. Secondly, by providing two counter-rotating thrusters and firing both at the same point (preferably simultaneously), the reactionary motive force applied to a satellite by each thruster in a direction tangential to the instant direction of motion of the thruster and the moment cancel out. While this may make it easier to calculate how to fire the thrusters in order to provide particular forces in particular directions, it does, however, have the disadvantage that some of the mass ejected by the thrusters is wasted; accurate calculation on the timing and orientation for thruster firing is, therefore, preferred. Further, in order further to provide for improved efficiency, one or more motors may be provided on a satellite to apply solar power harnessed from the solar panels of the satellite for the purpose of rotating the thrusters, either in conjunction with an energy source carried into orbit for this purpose or alone.
According to a modification, no independent motor need be provided to impart rotation to the rotating wheel 26. Instead, one or more thrusters can be oriented appropriately and fired for a sufficient time to impart rotation to the wheel. This provides a saving in payload mass carried into orbit, but a penalty in the amount of mass which must be expelled in order to impart the required rotation.
According to a further modification, power from the solar panels, which is both plentiful and predictable but difficult to harness in a way that enables it to be used for course correction in space, can be used to power motors to impart rotation to the or each platform carrying engines, thereby eliminating the need to carry any fuel payload for the purpose of rotating the engines. Further, given the 'renewable' character to the solar power, it would, if desired for any reason, be possible to halt rotation of the engines at all times other than those during which a correction is required to the orbit, powering the engines up once more using the solar power.
Because of the absence of air resistance, the only decelerating force on a rotating wheel upon which thrusters are mounted is the friction of the bearings. Achieving angular acceleration of a wheel, therefore, requires less power than on earth.
The above embodiments have been described with reference to circular trajectory, though this is not essential. The or each thruster may execute a path other than a circular path peripheral to a satellite. One example, shown in Fig. 4, is an elliptical path where, for example, kinetic is stored over part of the trajectory by springs and then converted into kinetic energy, and then back to potential energy and so on. This may be advantageous as, at two points along a trajectory of this or a similar type, there is greater acceleration - and these may provide more advantageous instances at which to fire the thrusters, thereby to gain additional increases in momentum of the expelled mass and, thereby, increased reaction forces on the satellite for expulsion of the same mass.
Embodiments of the present invention have been described and illustrated primarily with reference to their use in connection with the adjustment of a satellite orbit. The utility of the present invention is not, however, limited to this application and is more generally applicable to any other kind of engine which is used to derives momentum in a body from a reaction force applied to that body. Examples of other applications include motor cars, boats and aeroplanes.
Embodiments of the invention have been illustrated and described, variously, with the engine directed toward the centre of rotation or inwardly of the peripheral path executed by the engine by away from the centre of rotation. The angle of the axis along which fuel is expelled relative to the centre of motion is a parameter that can be varied to achieve optimum performance, dependent upon the application and circumstances of the embodiment in question.