Animation: Deltic Engine

The "Deltic" Engine was developed in the 1940s by Napier & Sons of Manchester, England to address the needs for high speed naval vehicles. The resultant engine had an excellent power-to-weight ratio, was compact by marine standards and was used in a variety of marine vessels. Two units were fitted in the famous "Deltic" type V locomotives (later class 55) used on Britain's railways between 1961 and 1981.

References:

The Deltic Preservation Society includes photos of Deltic locos, and some technical background.
The Deltic Design Page includes considerable technical detail of the engine in marine applications.
Napier Deltic Engine Training Manual from a marine hobbyist.
How Stuff Works, an excellent reference with animated diagrams showing how all sorts of things work.

The mechanism of the Deltic Engine is shown in these animations. The three crankshafts are arranged in a triangular structure (the Greek letter "delta", hence the name "Deltic"). On each crank are mounted two pistons, and each cylinder contains two pistons from adjacent crankshafts. The thermodynamic cycle of the Deltic engine is two-stroke.

Development of the Deltic Animation

Creating an animation of an internal combustion engine is relatively straightforward for straight-four and inline five engines:

The mechanism of a four-cylinder internal combusion engine. This is the engine found in most automobiles: four cylinders, each containing one piston. This arrangement of the pistons is chosen because of the way the engine works: the explosion of the petrol-and-air mix happens every second time the piston reaches the top of the stroke (The website How Stuff Works gives an amusing and informative description of how a four-stroke engine works).

The motion of the crankshaft is related directly to the animation clock. From that, the position of the conrod is calculated. The angle of the conrod is then calculated based upon its position, and the fact that the piston only has one degree of freedom. Once the angle of the conrod is known, the position of the piston is calculated. All this requires trigonometry, lots of paper and a sharp pencil. The observant will notice that the piston's motion is not perfectly sinusoidal: the lateral motion of the conrod causes deviations from the sine function in the piston's motion.

Applying several units together and putting more than one conrod on each crank introduces additional complexity. The source code was re-arranged to take advantage of the "Macro" features of POV-Ray. The detailed connecting rod between the crankshaft and the piston was the subject of many evenings of frustration. While the shape and the texture were relatively painless, getting the correct orientation required repeated calculations of trigonometry, particularly when a second piston was added to the crank.

Motion of two pistons on one crank. The most difficult aspect of the entire project related to the correct angle of the second piston on the crank. The solution was to define the motion of the second piston within its own coordinate space, and re-translate that into global coordinates at the end. The correct choice of sine, cosine or tangent functions was essential in getting the right phase.

My first attempt at the Deltic arrangement was made without reference to any official sources: just memories of discussions years earlier, and failures at modelling the same using LEGO® bricks. The intial angle between banks was set at 120° on the assumption that there were 18 pistons, thus three banks, and they must therefore be evenly distributed. The problem with this arrangement was that, although the top and right cylinders would meet and part, the left cylinder would oscillate without the gap between those two pistons growing or shrinking. "That won't work", I thought, so some research was called for.

A bit of research on the Internet revealed some interesting sources, including the maritime origins of the engine (it was not originally designed for railway use at all). Among the sources to be found on the Internet was a scan of the training manual, which included a drawing of the phasing gear-case (the bottom crankshaft indeed rotates in the opposite direction) and a "phasing and timing" chart (the offset per bank is a mere 20°). The training manual confirmed the issues I had found, and described the solution:

With an equilaterial triangular arrangement of the cylinders it can be shown that with two pistons in two cylinders in phase, the pistons in the third cylinder will be out of phase to the extent of 180° This can be modified by reversing the direction of one of the crankshafts (in practice the bottom one), the phase difference will then be 60°. This phase difference of 60° is divided equally between the three cylinders, making a phase angle of 20° of crankshaft rotation.

This means that one piston in each cylinder must lead the other by 20°. This lead is given to the exhaust piston, as an exhaust port lead is advantageous to the scavenging and cylinder charging process.

As the exhaust and inlet pistons in each cylinder are out of phase, port timing cannot conveniently be stated in terms of degree of rotation of the crankshaft to which each piston is attached, the exhaust piston is therefore taken as the datum, and the timing of both pistons referred to the crankshaft to which the exhaust piston is connected.

Complicated? No wonder I didn't get it first time! Attempting to use the offsets described in the training manual also failed, however, with results as before. The problem was that the synchronisation of the three crankshafts in the POV-Ray model also had to take into consideration the offset angle defined by the geometry.

One bank of a Deltic engine. By showing just one bank of the Deltic engine, the phasing of the pistons relative to each other can be shown. The correct phasing in the POV-Ray model was finally achieved by trial and error. This animation clearly shows the effect of the 20° phase angle the pistons do not meet precisely in the centre of the cylinder, but travel briefly in the same direction at the point of highest compression.

With the whole of bank 1 in phase, the phase of the remaining banks was relatively straightforward, with reference to the training manuals. A soundtrack of a Deltic railway locomotive in action was found on the web site of Henry Brugsch (who is blind). With his permission, a section has been included in the animations at the top of the page.

With the correct geometry, correct motion and a decent conrod, it remained to re-render the Deltic animation, with all 36 pistons and 18 cylinders on three crankshafts. The demo render of one cylinder bank (one triangle) uses the same code, with five of the six banks commented out of the source file. Rendering on a 500MHz PC took approx 4h 15min for 500 images. Compilation of the video from stills and the audio MP3 was performed with VideoMach, and typically took 10 minutes.

Other Internal Combustion Engines

The mechanism of an Inline Five (or Straight-Five)internal combusion engine. Here, five pistons are applied in series to produce an Inline Five engine. Each piston is offset from the next by 72 degrees. These engines run smoothly and quietly, and are used in a few production automobiles today (a few Audis and one Volvo). Different modellings of the crankshaft eccentrics have been used here.

Detail of V8 crankshaft and pistons. The V8 engine, popular for power in trucks and other road vehicles, is a simple extension of the concept of two pistons on one crank. This format is typically used to combine compactness and power (such as V8, V10 and V12 engines).

The Wankel Rotary Engine is a remarkable piece of design, and works on an entirely different principle. All the gory details may be found at Rotary Engine Illustrated (the animations of the rotary engine on that site are not my work).

Thanks to Henry Brugsch for the Deltic soundtrack and advice on audio browsers.