We are quite accustomed to seeing propellers in use as fans to circulate air on hot days or to circulate air over heating coils on cold days. We see boats and ships that are driven by propellers and when we see the propeller it is clear that it has two, three or four blades and that they are all twisted so that the propeller works by a sort of wedge action. The blades may be angled to the axis of the propeller shaft and as well as being twisted they may be raked and have other contortions like those used on a nuclear submarine where low noise is the essential requirement.
If a propeller is required to drive a boat and it is driven by an engine, the efficiency of the propeller becomes a very important element in the overall cost of operating the boat. This is an incentive to understand the propeller so that its design and application can be improved.
We need to understand how a propeller actually works. I have sketched out a flow pattern for a propeller running deeply submerged so that the presence of a free surface does not affect the flow. Water must flow through the propeller and this means that water in front of the propeller must be made to flow towards the propeller. This is possible because the pressure in front of the propeller drops producing a pressure gradient from distant points to the propeller. The result is a set of flow lines from every direction. I have attempted to show the flow pattern in figure 1. It cannot be accurate but it is not too far from reality.
Once the water reaches the propeller it enters the angled blades and the blades create a force on the water that is more or less at right angles to the blade. This force pushes the water backwards and makes it move in circles. As a result the water that leaves the blades is moving axially and rotating about the axis. This means that the water has kinetic energy that it did not have initially and this energy has been imparted to the water by the propeller. The water then moves at high speed away from the propeller and the flow pattern breaks down by mixing into a mass of swirls and eddies. The propeller experiences a force and it would move forwards if it could and the flow pattern would move with it.
We can see how the propeller works from its velocity diagrams. In figure 2 I have shown the blade having a curvature that is, of course, normal for full sized propellers. What is actually represented is a section of the blade all at the same radius. I have shown this section at some arbitrary angle and the rest of the blade will be twisted to have other angles. The propeller rotates so that the blade goes upwards on my diagram. This propeller will induce a flow of water towards it as I have shown in figure 1 and, because the blade is rotating, the water will, in fact, flow smoothly on to the blade as shown in the inlet velocity triangle. Now the blade, being curved, will divert the water to flow smoothly off its trailing edge as shown in the exit diagram. However because the blade is moving the water actually flows upwards to the right as I have shown. The water leaves at unchanged axial speed but with a substantial rotation whereas it came in axially. If you do not produce this rotation you get no thrust and so it follows that blades should be curved.
This raises the question of how do blades made from sheet brass work if all the sections are “flat”. Modellers and others make propellers in this way by silver soldering blades to a hub and twisting the blades. If it were to be possible for the water to flow smoothly on to the blade at inlet there would be no change in the velocity of the water relative to the blade between inlet and outlet and no rotation and no thrust. You could create these conditions in a water tunnel and the “propeller” would just free wheel like a child’s toy windmill in the wind. The propeller obviously works and it can induce a flow towards itself at inlet but when it does the velocity of approach of the water is such that the velocity relative to the blade makes an angle to the blade as I have shown in figure 3.
The water actually strikes the blade obliquely, which is not an efficient way to operate the blade, and effectively the blade is making the water behave as if the blade is curved. The water leaving the blade is rotating as before.
This shows that all propeller blades regardless of size should be curved for best performance. It is debatable whether these blades can be thought of as aerofoils. I think that one should recognise that propeller blades do not act alone as does an aeroplane wing; each blade is part of a group, even if it is one of two, and they share a flow pattern. The blades can be thin with fairly sharp leading edges.
In my velocity diagrams I have shown just one section of a propeller blade. What of the other sections? Obviously the tangential speed of any section depends on the speed of rotation of the propeller and the radius at the section and this can be calculated. The speed of the approach flow has been generated by a pressure gradient produced by the propeller and there is no reason to suppose that the speed that is generated varies much with radius. So the velocity diagram at inlet can be drawn for say the quarter points on the blade.
In figure 4 I have drawn the velocity triangles for sections of a blade at the quarter points of the radius of the blade. The approach velocity is the same for all the sections and the tangential velocity of each section is proportional to its radius. These can be added to give the velocity relative to the blade. Clearly the velocity of the water relative to the blade at these sections increases with radius and the direction of this velocity changes from 0° at zero radius to 90° at an infinite radius. These angles to the axis are easily calculated.
Now we have to look at the shapes of the blade at each section. For best performance these velocities should be tangential to the blades at their leading face. We know that every section must have curvature but we do not know how much curvature. We must take it that the water leaves tangentially to the blade at exit and I have drawn a typical exit diagram in fig 3. Clearly we can, within the mechanical constraints, choose the angle at exit. I do not think that there is any concerted view about what to choose. The velocity of the water at exit has two components, one axial and the other tangential. The tangential components taken over the length of the blade constitute a vortex with some relationship between the tangential velocity and radius. If you choose to make the tangential velocity proportional to radius the vortex is a “forced” vortex. In figure 5 I have drawn the blade shapes and the exit diagrams for a propeller producing a forced vortex at exit. It looks to be very practical. The tangential velocities are the four vectors up from the horizontal on the right.
So the basic design of a propeller seems to be quite straightforward but, as always, there is a complication. The thrust is produced by the change of momentum of the water as it flows over the curved face of the blade primarily as a result of the rotation. Inevitably there will be a higher pressure on the leading face than on the trailing face and this means that the water will spill over the leading face on to the trailing face at the tip to produce the normal tip vortex on a cantilever aerofoil or a hydrofoil. Figure 6 comes from website http://www.aip.org/pt/feb00/maris.htm. It clearly shows the rotating flow pattern that tells us that the propeller is producing thrust and it shows the tip vortices.
These vortices tell us that the flow over the blades is more complicated than the elementary theory. The propeller is a simple device in principle but something of a headache to design.
The foregoing has said nothing about whether the propeller set up in still water actually settles down to have the approach flow entering the blades tangentially, that is, in the best way. There is no reason why it should and it is a most unlikely outcome. So we have to look carefully at the propeller when we use it on a boat.
Now we have to try to use it on a boat. This introduces two further complications. They are that the propeller now operates near to the surface and secondly it moves relative to the undisturbed water. We have first to decide how the proximity to the free surface affects the flow pattern.
I cannot draw a flow pattern for this, because it would be too much of a guess. However in figure 1 the lines crossing the flow lines are for uniform pressure and necessarily the pressure drops as the flow approaches the propeller. If the propeller is near to the surface, say, one whole diameter below it, the surface will drop progressively to a lowest point above the propeller. Should that level be too low air may be drawn into the flow and the propeller is said to ventilate or cavitate. In the propeller the pressure of the water will rise as energy is imparted to the stream of water. After passing through propeller the water moves quickly and rotates but there is nothing to sustain this mode of flow. It must break down. The breakdown comes about by mixing between the flow from the propeller and the water surrounding it.
Figure 7 is of a jet of air emerging at high speed from a hole in the centre of a flat circular table. Two smoke pellets burning on either side show how the jet mixes with the surrounding air. Inevitably the jet widens as more air is entrained and the core narrows as the mixing spreads to the centre. The result is a much larger mass of air moving more slowly with the same momentum all in fine-grain eddying motion.
The plume of water from the propeller must behave in some similar way. The water from the propeller will move much more slowly than the jet of air and will break up into larger eddies and these may break the surface to give a confused eddying wake. That will rise above the original surface level. These changes in level and the propeller wake can be seen in figure 8 but here the surface tension has smoothed out the surface.
Now we have to think about the consequence of the forward motion of the boat.
There is no reason to suppose that the forward motion suppresses the flow pattern caused solely by the rotation of the propeller. Then the forward motion will add directly to the speed at which the water approaches the propeller. We now need to decide what determines the final steady state.
If, say, my steam launch were to be at rest I could open the throttle fully and watch the outcome. It is easy to see the establishment of the induced flow pattern as a fall in level in front of the propeller and the creation of a wave behind the stern. The launch accelerates. If the engine/propeller combination is correct for top speed then the propeller cannot be operating with tangential flow at inlet during the acceleration phase. As the speed increases the velocity of the approach flow increases and the angle of the relative velocity at inlet to the propeller changes and the change continues until the thrust produced by the propeller is exactly equal to the resistance to motion of the boat. There is nothing to cause this speed to be the speed at which the propeller has tangential flow at inlet. We have to match the boat, the propeller and the engine and gearbox to produce that result.
This may be disappointing but it is a fact of engineering. We must find ways to make the process easier. However, before we go there, we have to decide what happens if the propeller can drive the boat so quickly that there is no time for the ordinary hydrostatic pressures to create the static flow pattern and the speed at inlet is equal to that of the boat. In the limit the propeller lifts half out of the water and just cuts lumps out of the water with the immersed half and throws them into the air sideways and backwards. It is not pretty, it is not efficient but it looks exciting. I have had so little opportunity to observe it that I cannot offer any insight to it.
If we are to match a hull to an engine and a propeller the cheapest item to change is the propeller so we must concentrate on that. It is much facilitated by the concept of pitch. This can be coupled to diameter and to the generic shape to give ranges of propellers from which to choose.
In figure 7 I have shown two sets of three model propellers. The metal ones have been fabricated and the blades twisted to profile after assembly. The plastic ones have been moulded. Both sets have been made to have some blade shape that is deemed by the designer to be correct according to some “theory”. (I do not use this word in a critical sense but to point out that unless some criteria are devised for the way the propeller is intended to work it is hard to describe the shape geometrically.) The plastic ones have their pitches moulded into one of the blades in millimetres.
We need to have some idea what the yardstick might be. Well this device is often called a water screw and this goes back to the first propellers, which were in fact a short length of Archimedean screw. Archimedean screws were and still are used in some places in use for raising water. A diagram from Wikepedia is shown in figure 8. It is clearly a helical surface inside a tube. In one revolution water is moved along the tube by the pitch of the helix.
A helix is a geometrical figure created by a radial line rotating about an axis and simultaneously moving along the axis.
I tried making a diagram and then decided it would be better to make a model of a helix from a piece of dowel and some cocktail sticks. It is shown in figure 9. The sticks lie on a helical surface and they look very like a propeller. Clearly the helix is a good, and probably the only sensible, basis for the design of a screw propeller.
However if a propeller were to be made as a true helix it would have no curvature to the blades. I made another wooden model with a curvature and it is shown in figure 10. Close inspection shows the curve at the root.
People like exploring the possibilities of the geometry of these blades and all sorts of blade shapes have been devised but they all quote the pitch as one basic dimension the other being diameter. The pitch they mean is the pitch of the helix, that is, the advance per revolution of this geometrical figure. In my two wooden models the pitch is the same, it is the angular spacing that is changed from the first to the second.
So we can have a variety of designs and for each design there will be a range of diameters and a range of pitches for each diameter. This starts to look very expensive for a manufacturer and the total number of different propellers in the range is reduced to what makes commercial sense. It is fortunate that the screw propeller performs quite well when operating off the optimum conditions. The operator of the boat has to make the best match that he can.
If the speed of rotation is multiplied by the pitch of the propeller, the result has the units of speed and can be compared with the actual speed of the boat that it drives. The difference is called the slip and the ratio of the two speeds is, in some way, a measure of the functional efficiency of the propeller. We might reasonably ask what factors determine the slip.
We have seen that the approach flow to the propeller on a moving boat is made up of the boat speed and the induced speed. Inevitably the slip will be at least equal to the induced speed. So propellers with no slip may be possible when the speed of the boat is too high for there to be enough time for the induced flow pattern to form but not at the speeds of displacement boats. Practical values for slip vary between 5% for light boats and 25% for heavy work-boats.
There are all sorts of sites on the net that give practical ways of finding a matching propeller for a given set-up of engine, gear-ratio and boat.