In 1938, the power at altitude was calculated from empirical formulae developed at the RAE, which were suspected of being inaccurate, and to over-estimate the power at altitude, particularly in regard to the full-throttle height.
With my colleagues A. Yarker, H. Reed, G. L. Wilde and W. O. Challier, I started in 1938 to develop new and more accurate methods of power assessment to account for the discrepancy between the predicted aircraft performance, mainly of the Spitfire and Hurricane, and the inferior performance actually measured.
There was also a second important reason for this work, namely, a correct understanding of how the combination of engine and supercharger worked, so that more power could be obtained from the engine, by developing more efficient superchargers and correctly matching their capacity to the engine requirements.
Let us consider a typical cylinder as illustrated diagramatically in Fig 1, and start from the condition at the end of the exhaust stroke, when the piston is at top dead centre, the exhaust valve is about to close and the inlet valve to open. The residual exhaust gases in the clearance volume S, have a pressure Pe, which, with open exhaust pipes, is equal to the outside ambient air pressure.
The exhaust valve now closes and the inlet valve opens, and a new charge rushes in from the induction pipe at boost pressure Pc, compressing the residual exhaust gas to a volume Pe/Pc.
At the end of the suction stroke, the cylinder is charged with air/fuel mixture (93% air and 7% petrol by weight) at the boost pressure Pc and charge temperature Tc. Since the Merlin had a compression ratio of 6:1, meaning that the total volume of the cylinder was six times the clearance volume S, the total volume of charge inhaled was
and since the density of the charge is proportional to Pc/Tc, then weight of charge inhaled per stroke is
If the engine is rotating at N rpm, and with the dimensions of the Merlin cylinders (6 in stroke, 5.4 in diameter, 12 cylinders), we arrive at the following equation for the charge consumpton per minute
In this equation, it is convenient to measure Pc and Pe in inches. Hg, and Tc the charge temperature in °K. On the test bed, Pe would be equal to atmospheric pressure, namely 30 in Hg.
Hence, on the test bed,
It is easy to verify this equation by running the engine on the test bed at constant rpm (and hence constant Tc) and varying values of Pc. The charge consumption is linear with boost pressure at both 3,000 and 2,200 rpm, and is zero when the boost pressure equals 5 in Hg. Many similar tests were done, all of which verified the above equation.
We now need to know the absolute value of the charge temperature Tc. On the Merlin engine the air is first sucked through a carburettor where the fuel is sprayed, and the evaporation of the fuel has a cooling effect equivalent to-25°C. This mixture then passes through the supercharger where it is compressed, with a corresponding temperature rise Δ T, given by
where U is the impeller tip speed in ft/sec. Thus, the temperature Tci of the charge as delivered into the induction pipe is:
where Ta is the temperature of the air entering the carburettor.
Now, in passing from the induction pipe into the cylinder, the charge moves through the hot cylinder head and through the very hot inlet valve, and a certain amount of extra temperature is thereby picked up, with more added by the residual gases.
To determine the actual temperature in the cylinder, we must again have recourse to experiment, and run an engine on the test bed where we can measure the weight of charge, the rpm, the boost pressure and the back pressure, and thus determine the effective charge temperature Tc from the formula:
The results of these experiments are given in Fig 2 where the charge consumption in the cylinder, calculated from the above equation, is plotted against the boost temperature in the induction pipe. The shaded area shows the amount of temperature picked up by the charge in its passage through the cylinder head and inlet valves. A good approximation to the charge temperature in the cylinder is given by:
which fits almost exactly the experimental result shown at the top of the shaded area.
We have now reached a point where for any given air temperature at inlet to the carburettor (i.e. at any altitude or climatic condition), and for a given tip speed on the supercharger (which depends upon the gear ratio driving the supercharger and the rpm of the engine) we can calculate the induction pipe temperature from the formula:
Having determined in this way the induction pipe temperature, we can refer to Fig 2, and obtain the charge temperature, Tc, in the cylinder.
Knowing the boost pressure and the back pressure and the rpm of the engine, we can now calculate the weight of charge which the engine will absorb under any flight conditions.
So far, so good, but we now have to face the problem of how we move from knowing the charge consumption to calculating the brake hp of the engine.
We must return to the test bed for more information concerning the relationship between the consumption of charge and the power output of the engine.
We make the initial assumption, which we shall check later, that the gross hp developed in the cylinder, referred to as the indicated hp (ihp) is proportional to the charge flow.
We also note that the gross hp is equal to the brake hp of the propeller plus the power required to drive the supercharger plus the frictional losses in the engine. Thus,
The power required to drive the supercharger is well known to be
(allowing for the efficiency of the supercharger gear drive) where ΔT is the temperature rise in the supercharger due to compression. At a given rpm the indicated hp is proportional to the weight of charge, as is the supercharger hp, and both are proportional to (Pc - 5) at sea level.
Hence, if we plot the power of the engine measured on the test bed at a given rpm by varying the boost pressure and extrapolate the curves to a boost pressure of 5 in Hg, where the ihp and the supercharger hp are both zero, we shall obtain the hp which represents the frictional losses, and these losses will be proportional to N2, where N is the rpm of the engine. An example of this is shown in Fig 3 where it will be seen that at 3,000 rpm and for two different supercharger gear ratios, the frictional hp is 210 when Pc = 5, i.e. when the charge weight is zero, and, hence, the ihp and the supercharger hp are also zero.
Returning now to the equation ihp = bhp + supercharger hp + losses, for the Merlin engine this can be written:
By running the engine on the test bed we can measure the weight of charge consumed, the bhp produced, and calculate the supercharger power and the frictional losses. As a consequence, we now know the ihp per lb of charge, and the results of many tests are condensed into the unique curve shown in Fig 4, where it is seen that, for every lb/min of charge consumed, the engine produces 10.5 ihp. This particular value applies over a wide range of engine speeds from 2,200 to 3,150 rpm, and over a wide range of charge consumptions and varying supercharger gear ratios.
The problem of determining the power, therefore, at any flight condition is now solved. We can determine the charge consumption as previously described, and, hence, the ihp by multiplying the consumption by 10.5. Knowing the supercharger tip speed we can calculate the power absorbed by the supercharger, and knowing the rpm, we can get the frictional losses. By subtracting the supercharger power and frictional losses from the ihp, we obtain the bhp on the propeller.
In Fig 5, a comparison is shown between the above method of calculating the hp, and the power as actually determined in a Hurricane II, No. P3269, calculated from the aircraft speed and drag, and the agreement now is quite remarkable.
I have dealt with the problem of determining the hp of the Merlin engine in flight in some detail, because so far as I am aware, this is the first time that the results of these experiments have been published, and although at the time it was “all in a day’s work”, looking back, I and my colleagues can now see its importance, since the formulae described above were used to design the two-stage Merlin supercharger with its after-cooler, and to calculate the power that such an ar
rangement would give.
By examining the formula for the charge consumption, namely:
we note that the engine charge consumption (and, hence, its power) can be increased either by increasing the boost pressure, Pc, or reducing the charge temperature, Tc, or, better still, by doing both.
These features were behind the conception of the two-stage after-cooled supercharger fitted to the Merlin 61 engine. To raise the boost pressure, Pc, particularly at altitude, we fitted an extra supercharger which literally supercharged the supercharger, and, at the same time, in order to reduce the charge temperature, Tc, we fitted a water-cooled intercooler to cool the charge.
Fig 6 shows the increases in power obtained from the Merlin engine by the various stages of this work. It shows the power produced by the original Merlin III, as fitted to the Hurricane I at the beginning of the war, and the power of the Merlin XX which was subsequently fitted to the Hurricane II.
Thus, the power of the Merlin III engine at 20,000 ft was increased from 860 hp to 1,060 hp for the Merlin XX. If we look now at the power of the Merlin 61, which was fitted with the two-stage blower plus intercooler, we note that the power of the engine was increased at 30,000 ft from 510 hp to 1,060 hp by this series of supercharger developments.
The Merlin 61 was never, unfortunately, fitted to the Hurricane. These engines were reserved for Spitfires, Mosquitoes and Mustangs (and a few Lancaster Pathfinder bombers). However, we can see the effect of fitting the Merlin XX to the Hurricane by looking at Fig 7, and note that at 20,900 ft its speed increased from 300 mph (more was claimed at the time!) to 330 mph.
The Hurricane’s role thus became that of a bomber killer at about 20,000 ft, and later, a ground attack aircraft, and many different marks were made, yielding an extremely versatile aircraft. Even tank-busting cannon were fitted.
The Spitfire, on the other hand, was paramount at high altitudes as a fighter-to-fighter aircraft, and the effect on its performance of the engine development is shown in Fig 8, where about 10,000 ft was added to its fighting altitude, and something like 70 mph to its top speed. These gains came at a time in the war when the odd extra thousand feet and extra speed meant the difference between death to the enemy fighter or death to the Spitfire.
I have talked of the development of the supercharger, and the increase in power which this gave to the Merlin engine. This was made possible only by the design and development work on the engine itself which fitted the jigsaw of carburettors, the two centrifugal compressors, intercoolers, coolant circulating pumps, and so on, together in order that the engine could still be installed in existing aircraft, and the numerous modifications which had to be designed and tested in order to make the carcase of the engine mechanically reliable at the greatly increased powers which were being used. At this time the Chief Designer at Rolls-Royce was A. A. Rubbra, and the Chief Experimental Engineer (who was my immediate boss) was A. C. Lovesey.
It was a great education and privilege to work under these two men, and I like to think that it was their expertise and guidance which made possible the translation of Hooker the Applied Mathematician, to Hooker the Engineer.
Needless to say, there were many others who made great contributions to this programme of Merlin development, and we all worked under the constant encouragement and drive of Hs.
To illustrate the use of the preceding equations let us calculate the bhp of the Merlin in a Hurricane aircraft. The data we are given is as follows:-
rpm 3,020
Altitude 21,000 ft
Pc Boost Pressure 48 in Hg
Pe Back Pressure 20 in Hg
Aircraft Speed 330 mph
All the above were measured in the aircraft during flight, and we require to calculate the engine bhp.
From the standard altitude tables, we know that the ambient air temperature at 21,000 ft will be 246°K. To this must be added the temperature rise of the air entering the carburettor due to the forward speed of 330 mph. This is given by the simple formula
Thus the temperature of the air entering the carburettor is
From this must be subtracted 25°C due to the evaporation of the fuel, and thus, the air entering the supercharger is at a temperature of
The engine has the high gear ratio drive to the supercharger engaged (9.29:1), and since the diameter of the impeller is 10.25 in, the tip speed U is
The temperature rise through the supercharger is given by
Thus the temperature Tci of the charge in the induction pipe is
The final charge temperature Tc, which includes the heat picked up from the valves and ports is
Returning to the equation for the charge consumption, viz:
Hence the ihp at 10.5 hp per lb/min
From this must be subtracted the frictional horsepower and the power to drive the supercharger.
The frictional power is 210 hp and the power to drive the supercharger is
Thus the bhp equals
ihp - supercharger hp - friction hp
This figure agrees remarkably with the bhp calculated from the aircraft drag, as shown in Fig 5.
First published in 1984 by Airlife Publishing, an imprint of The Crowood Press Ltd, Ramsbury, Marlborough, Wiltshire, SN8 2HR
www.crowood.com
This e-book edition first published in 2011
© Sir Stanley Hooker 1984
All rights reserved. This e-book is copyright material and must not be copied, reproduced, transferred, distributed, leased, licensed or publicly performed or used in any way except as specifically permitted in writing by the publishers, as allowed under the terms and conditions under which it was purchased or as strictly permitted by applicable copyright law. Any unauthorised distribution or use of this text may be a direct infringement of the author’s and publisher’s rights, and those responsible may be liable in law accordingly
ISBN 978 1 84797 325 2
Not Much of an Engineer Page 30
