The lack of a 90 degree bank angle means a balance shaft is required, and the 144 degree bank angle potentially means there are simultaneous ignitions, assuming each bank is configured as a normal 5 cylinder and the crankshaft is the common pin type.
All of that means the firing order needs attention. The usual (for the VAG and Chrysler engines) is to fire each bank as 1-5-2-3-4 at intervals of 144 degrees, with the corresponding cylinder in the opposite bank firing immediately after (either 72 degrees or 90 degrees later, depending on the bank angle and whether "split pins" are used on the crankshaft). I.e. cylinder 1 in the left bank, then cylinder 1 in the right bank, 5L, 5R, 2L, 2R etc.
The Viper / SRT10 uses a 90 degree bank angle and common big-end crank pins, which means opposite cylinders fire at 90 / 630 degree intervals, and the overall ignition intervals alternate between 90 and 54 degrees (uneven firing) - no balance shaft, only crank counterbalances. Something like the old V10 Audi S6 and S8 use a split pin crank in a 90 degree V10, giving intervals of 72 / 648 between opposite cylinders, and 72 degrees between every ignition (even firing) - it requires a balance shaft. The LFA uses a common pin crank in a 72 degree block, and a different per-bank firing order (the usual inline 5 order, below) - it has no balance shaft, again see below.
With either narrow-angle setup, whilst it has been proven that the sequential firing of opposite cylinders is kindest to the crankshaft (discovered with aero engines in the second world war), there really isn't much of an option to try anything else due to the mechanics of the configuration (10 unique piston phases; compared with 6 for a typical V12).
In the case of the Tomahawk, the 5 cylinder banks are interleaved at 144 degrees, which is the firing interval between cylinders in either bank and, as already stated, this means two cylinders must fire at the same time if a common pin crank is used. This is typically disastrous for crank longevity (also discovered with aero engines during the second world war) unless you can find a firing order which minimises the cyclic stress on the crank. This has historically proven to be of interest even in a race environment (BRM's H16).
The rationale for the 1-5-2-3-4 firing order within a bank is that it maximises the primary imbalance and minimises all other imbalance; a primary imbalance can be tackled with a single crank-speed balance shaft (or simpler crank counterbalances in a 90 degree block), whereas you need various complicated arrangements for higher order imbalance. Crank torsion from gas pressure is really much the same for any 5 cylinder firing order, but this firing order has substantially lower inertial torsion, which is ideal for a high revving engine and smooth idle.
The usual firing order in an inline 5 is actually the one that minimises the primary imbalance (1-2-4-5-3), but no balance shaft is needed with the typical displacements found there, as the secondary imbalance is comparatively small anyway (also LFA). Inline fours have a secondary (more precisely: second order) imbalance, and that's why their balance shafts (originally only used on larger engines) spin at twice crank speed, imparting huge inertia and friction as a result. This is not ideal in a race engine (also LFA).
Using a split-pin crankshaft with a 144 degree bank angle leaves two possibilities: advancing the second bank to regain the true 72 degree intervals and so that opposite cylinders fire sequentially (best for torsion), or delaying it further. The delayed option is best for the central exhaust pairing, but the torsion is a larger problem, I feel and overrides this benefit. Furthermore, a common pin crank is stronger and more rigid, so the reduced torsional excitation benefit of the advanced split is probably negated by the reduction in rigidity and strength of the resultant crankshaft, especially with such a large split angle (72 degrees, larger than any production engine).
So a few things are a given:
- The 144 degree separation of the banks.
- The use of a common pin crankshaft.
- Simultaneous ignitions.
- The likely use of 1-5-2-3-4 within each bank.
So the task now is to find which cylinders fire simultaneously, which can be done by looking at the usual firing order for 72 degree intervals:
1-6-5-10-2-7-3-8-4-9
Then offsetting by delaying the second bank to 144 degrees instead:
1-5- 2- 3-4
9-6-10-7-8
And so the 5 simultaneous ignition pairs are: 1,9; 5,6; 2,10; 3,7; 4,8.
These pairings are probably not too bad in terms of crank torsion, given they are almost symmetrical and closely follow the torsion-friendly individual bank firing order.
Looking at the picture, the exhaust pairings are: 1,2; 3,4; 5,10; 6,7; 8,9.
This gives three lots of 144 / 576 intervals and two lots of 288 / 432.
That is a very unusual setup, but should sound very interesting at low engine speeds - hints of 5 cylinder, boxer four, V8 and even six cylinder growl. At high rpm, it'll just sound like a MotoGP bike, as already stated.
I investigated other firing orders to see which would complement the exhaust layout better (consistent and widest possible intervals for each pipe; the 5,10 pairing will always be 144 / 576), but each one was worse for both the balance aspect and the crank torsion aspect. So this exhaust configuration is likely only for aesthetic reasons, and "just because" (and because AES allows it, without the need for recordings).
A simple swap would be to pair 4,5 and 9,10 leaving 3,8 across the banks, giving four lots of 288 / 432 and one 144 / 576; this would sound sweeter, in my opinion. This is actually how Audi packages its V10 exhausts in front-engine applications, see
here.
Using the usual 5 cylinder firing order of 1-2-4-5-3 results in each pipe getting 144 / 576 (only a little tight for pulse tuning), and remains a possibility if a balance shaft is to be avoided, even though the simultaneous ignitions from a common pin crank might end in disaster.
If I could get at the AES file once the car is added to the game, I could confirm the firing order easily.