The argument

1Both cranks fire evenly

The first thing to give up is the intuition that a cross-plane V8 fires unevenly. It does not. Neither does a flat-plane one.

Eight cylinders, four strokes, 720° of crankshaft per cycle. 720 divided by 8 is 90. Both engines put a power stroke on the flywheel every 90° of rotation, eight times per cycle, perfectly spaced. Hook a torque transducer to the output shaft and there is nothing there to tell them apart.

Which means the burble is not coming from the firing interval, and every explanation that starts “because it fires unevenly” is wrong about the one part it is trying to explain. I gave that explanation for years.

2What a bank hears

An engine does not exhale through its flywheel. It exhales through two exhaust manifolds, and a manifold is not bolted to an engine — it is bolted to four cylinders, and those four are all it will ever hear.

So take the even 90° train and throw away the half belonging to the other bank. What is left depends entirely on where the throws are.

A cross-plane bank coughs twice in quick succession, waits three quarters of a turn, and coughs again. The other bank does the same thing out of step, the two trains beat against each other, and the interference never resolves. A flat-plane bank exhales in even thirds of a revolution; both banks lock in phase and the harmonics stack cleanly at twice the frequency.

Four numbers on a crankshaft. Everything else in the project exists to make that audible.

3The forging is the input

A firing order is not a design input. It is a result. You forge a crank, you hang eight rods on four journals, you grind a cam that decides which cylinder on each pin fires on the first revolution and which on the second — and the order is whatever falls out. Ford and Chevrolet got different orders from identical forgings for exactly that reason.

So this is all the program is given. A bank angle, four throws, eight rods, and which revolution each one takes.

Crankshaft{
    90.0_deg,
    { 45.0_deg, 315.0_deg, 135.0_deg, 225.0_deg },
    {{
    //  cylinder    journal   bank          revolution
        /* 1 */     { 0,      Bank::right,  0 },
        /* 2 */     { 1,      Bank::right,  0 },
        /* 3 */     { 2,      Bank::right,  1 },
        ...

It refuses to build a crank that cannot exist — two rods on one journal, a bank that does not add up — and then it tells me what I have made.

  ---- everything above was specified. everything below came out. ----

CRANKSHAFT
  forging              cross-plane
  firing order         1-5-4-2-6-3-7-8
  the engine fires     every 90 deg, eight times per cycle

WHAT EACH BANK HEARS
  A manifold is not connected to an engine. It is connected to four
  cylinders, and it only ever hears those.

  right bank   cyl 1 4 2 3   fires at   180 -  90 - 180 - 270
  left  bank   cyl 5 6 7 8   fires at   270 - 180 -  90 - 180

  LOPSIDED. Each bank coughs twice in quick succession, waits three
  quarters of a turn, and coughs again. The two banks are out of step
  with each other and the interference between them never resolves.
  This is the burble.

1-5-4-2-6-3-7-8 is what is cast into a 1968 302 intake manifold. It was never typed in, and the day it first appeared there I went and checked the casting to make sure I had not fooled myself.

4Same forging, different cam

Fit the 1982 5.0 H.O. camshaft to the identical crankshaft — which is exactly what Ford did — and the order becomes 1-3-7-2-6-5-4-8, the 351W order. The cam moved which cylinder on each pin takes the first revolution. It did not move a single throw.

Same crank, different cam, different firing order, identical sound — because the sound was never in the cam.

This is the sharpest test the model faces and the reason the firing order had to be derived. A lookup table would have produced both orders correctly and learned nothing from either.

5What the burble cost

If the flat crank breathes more evenly and sounds better, then why did Detroit forge the other one eight million times. Ask the same rod table a different question and it tells you.

      looking down the nose of the crank

                   O             
                   .             
                   .             
             O.....+.....O       
                   .             
                   .             
                   O             

  shaking, at 3000 rpm, from 0.78 kg of reciprocating mass per bore:

               force        couple        traces
  primary         0 N       1032 Nm     a circle   counterweights take it
  secondary       0 N          0 Nm     nothing

  NOTHING LEFT OVER. The secondaries cancel each other exactly, and
  the primary couple traces a circle, which is a rotating imbalance, which
  a counterweight can be drawn to oppose. The engine holds still. It will
  idle at 600 rpm on soft mounts without walking across the bay.

  This, and not the noise, is why Detroit forged crosses.

A piston does not travel sinusoidally, so killing the once-per-turn term with a counterweight leaves a twice-per-turn one behind, and nothing bolted to a shaft turning at ω can cancel a force at 2ω. On the cross-plane crank the secondaries cancel each other outright and the primary couple traces a circle, which a counterweight can be drawn to oppose. On a flat crank they trace a line. Half a tonne of force, a hundred times a second, and a line is not something you can chase with a rotating weight.

The flat crank sounds better and shakes. That is the bill, and it is why almost nobody pays it.

6Two microphones, because there are two pipes

A V8 does not have an exhaust. It has two, down opposite sides of the car, permanently out of step on a cross-plane crank. So the recording is made the way it would be made in a car park: two microphones 0.6 m apart, 1.5 m behind two tailpipes 1.0 m apart, each microphone hearing both pipes — quieter by the extra distance, later by the time sound takes to cross the gap.

Nothing is widened or panned. The image is the geometry, and moving the microphones moves it.

The thesis lives in crankshaft.hpp and the balance argument in balance.hpp. If changing the crank ever stops changing the sound, the model has quietly stopped being true and the project is over. How I check that it has not →