The One-Stroke Engine Revisited

Years ago I wrote about the one-stroke engine, which is a proper description for any type of gun. Because its fuel and oxidizer are both contained in the solid propellant, it has no need of an intake, compression or exhaust stroke. All that remains is the power stroke, which accelerates the “piston” or projectile to very high speed.

You meet fascinating people at the races – at Laguna Seca one year I found myself in conversation with a retired Israeli automatic weapons designer, and owner of a Honda CBR600RR. When I asked him what the pressure-versus-volume curve for a gun looked like, he smiled tolerantly and said, “You know very well what it looks like – it’s just like the P-V diagram for an IC engine.”

In both cases the curve rises steeply to maximum as combustion generates hot, high-pressure gas in the cylinder. In a gun, this pressure is close to 50,000 psi, and in an IC engine at peak torque it is more like 1,200 psi. As the projectile, or piston, begins to move, pressure falls as the gas expands. When the exhaust valve opens or the projectile leaves the muzzle, the remaining pressure is vented to the atmosphere.

Of particular interest is the similarity of guns and IC engines when it comes to where their energy goes. In an IC engine, approximately a third or less of the total appears as work at the spinning crankshaft, and in a gun the figure is said to be close to 32 percent. Both the IC engine and a gun put another third of their energy into hot gas that no longer has enough pressure to do useful work. Finally, if you briefly contain a hot combustion process inside a metal container, that container will get hot – this is heat loss. In both cases again, IC engine and gun, this loss is roughly 30 percent.

When the US Navy took on the task of defending its Pacific fleet in World War II against attack by enemy carrier planes, its engineers knew that long periods of continuous firing would be required, as the guns tracked incoming aircraft. Without active cooling, guns become rapidly hotter until they ignite their ammunition on contact. Therefore you will see water-cooling jackets silver-soldered onto the barrels of the 40mm Bofors guns that did most of this work. You can see them in YouTube videos, steadily pounding away as their crews push one after another multi-round clip into their top feeds

Many dragster engines just absorb the heat of a single run in their own mass, and cool between rounds. Engines that run longer have cooling systems capable of carrying away unwanted heat as fast as it is generated.

Why can’t we recover some of that one-third of combustion energy release that leaves in the form of hot exhaust gas? This gas is very hot, but its pressure has fallen too low to do significant further work pushing pistons or projectiles. How can we stop some of this waste? If engine operation were continuous over long periods of time, we could recover that heat to raise steam, as is being done in the latest combined-cycle gas turbine electricity generating plants (whose conversion efficiency is now pushing 60 percent). Starting such a plant and getting the steam cycle up and running takes several hours, so we can’t expect to see such a “bottoming cycle” applied to light-duty vehicles such as cars and motorcycles.

The hot gas produced by gunfire has been a serious problem for some military aircraft, as the oxygen-free inert gun gas can stall jet engines that inhale large volumes of it. The long barrels of high-velocity tank guns can contain enough such gas after firing that when the loader opens the gun’s breech to insert the next round, crew inside the tank are “negatively affected” by the gas. Therefore you will see a bore evacuator device, a round enlargement of the barrel at about its midpoint, to clear hot gas from the barrel between rounds.

One of the most dramatic effects of the firing of guns is their recoil – whether of a pistol, a rifle, or an artillery piece. How much energy is consumed by recoil?

Every other town has a wartime artillery piece on display as a veterans’ memorial. The numbers for the one in our town give the answer. When a gun fires, the combustion gas is like a powerful coil spring, with one end pressing against the projectile, and the other against the closed breech of the gun. Experience shows that momentum is conserved – the mass of the shell, multiplied times its muzzle velocity, will equal the mass of the gun tube, times the velocity with which it is thrown back in recoil. But energy is not equal between the two, for it is proportional to velocity squared. The barrel weighs over 40 times more than the shell, but because the shell’s velocity is so high, it gets most of the kinetic energy, leaving only a couple percent wasted as recoil.

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What about friction? Because a gun just accelerates a piston and has none of the IC engine’s mechanism to convert back-and-forth piston motion into crankshaft rotation, it has very low friction, estimated at 2 percent. The added friction of an IC engine’s bearings, cams, and gears eats up more like 15 percent at highway speeds. This is treated as a part of loss to the cooling system.

It is a common idea that the back-and-forth motion of pistons and valves is of itself a loss – that the energy used to accelerate a piston or valve is not recovered when it slows, stops, and reverses. Many loyal “Ducatisti” fervently believe that the desmodromic (springless) valve drive used in that maker’s engines saves vast amounts of energy, making them much more powerful. Sorry, in both cases ‘tain’t so. Energy is neither created nor destroyed – in any process, the energy totals before and after are equal. When the four pistons of a flat-crank in-line four-cylinder engine are at their highest speed they can be moving at nearly 100 mph. A quarter of a revolution later they are all stopped at either TDC or BDC. 

Where did all their kinetic energy go? Minus the friction required to transmit the forces through bearings, it causes the crank to speed up. In the next quarter revolution the pistons are again accelerated to maximum speed, and the energy to do this comes from the crank, which slows down. This rapid, twice-per-revolution fluctuation in crank speed is what upset rear tire traction in Yamaha’s early M1 MotoGP bikes, resulting in less tire grip and less acceleration. When engineer Masao Furusawa changed the crank’s firing angle from 180 degrees to 90, two pistons were at maximum speed when the other two were stopped, so the pairs of pistons exchanged energy with each other rather than with the crankshaft. The result was a smoother delivery of torque to the rear wheel – and a MotoGP championship for Valentino Rossi in 2004.

When a valve spring is compressed during valve lift, energy is stored in the spring. When the spring expands in returning the valve to its seat, that energy is recovered, minus the excess friction produced by spring pressure. Provided the cams rotate fast enough to produce full oil films, valve-train friction is quite small. It is at idle and very low engine speeds that valve-train friction in valve-spring engines increases steeply from the partial breakdown of cam-to-tappet oil films. This has caused some automakers to adopt roller cams to slightly improve commuter-speed fuel mileage. A desmo system shines here because there is no valve-spring pressure to cause partial breakdown of oil films at low speeds. At high engine rpm, the major loads are those required to accelerate and decelerate the valves themselves, so the resulting difference in high-speed friction loss between springs and desmo is small.