"Idle Curiosity about my game mechanic" Topic

Here is a problem for an idle moment…

As you may have seen I'm tweaking my Battle of Britain rules. I use the Spitfire as the basis for stats. I wrote it as the 'way the system works', and then extrapolated the other aircraft from that.
For instance there are three phases in a bound, so the Spitfire has a max speed of 9 – 3 moves in each phase. This gives me a Bf109 of Max 10, Hurricane of 8.

Each phase is 3 seconds.

Firing is as follows.

Start with -Range mod +/- Aspect mod + Guns +d6

A Spitfire carried 14 seconds of ammo, which was fired in 3 second bursts* (hence phase length), so that is 5 shots, 4 at +3, and the last at +2.

For the 109 I have 9 seconds (3 phases) of Cannon and Mg fire, then another 9 seconds of Mg fire after the cannon was empty.

There were just 2 MGs firing on interrupter through the prop.

The firing profile of the 109 is
+5 / +5 / +5 / -2 / -2 / -2

SO, given the MG pair is -2, what is the Cannon with no MG? (and no, it isn't +7!, the MGs aren't actually reducing their effectiveness.)

To be clear, I am not looking for any suggested amendments, the game works well as it is. This is just idle curiosity.

*RAF pilots would have the tracer every 3 seconds to help them count usage. The last 2 seconds often had a lot of tracer to say "You're out!"

Center-line weapons were more effective then wing mounted weapons. How much is up to you.
Don't forget crew quality.

Given the numbers and firing formula as presented, I don't see how the cannon can be anything but +7, if not more.

If firing the MGs is actually a negative modifier (-2), wouldn't our plucky BF 109 pilot be better off not firing them at all and just engaging the Spits with his Luger?

I think I understand what you are trying to capture with the – 2 mod, but I can't make the maths work in my head when combining it with the positive mod for the cannon. Perhaps the cannon should be resolved separately.

Here's a story for your nasty Bf109 – 20mm cannon:

THE BATTLE OF BRITAIN LONDON MONUMENT – 43 Sqn RAF

Uncle Alan was extremely short (see photo on page).

After landing his hurricane, his ground crew helped him out and pointed out a bullet-hole in the armour-plating, just above his head.

It ought be noted that the 20mm cannon could fire AP as well as HE.

The only thing I can add is that there is a difference in the results of the nose and wing-mounted guns, concentration, and effective firepower. Also, the ability of the pilot to put the pipper on the target and keep it there long enough is one of the most variable factors of air gunnery.

Wing guns are harmonized to converge at a "sweet spot" where all of the rounds will be on target if the aim is correct. At longer and shorter ranges, depending on the harmonization, the wing guns on one side will completely miss. In a worst case 50%.

At very short and long ranges the pilot needed to offset the pipper to aim using the guns from only one wing. So the effective firepower is 50%. Nose-mounted guns do not have this problem.

However, since you will naturally have a greater dispersion with the wing guns there is a slightly greater chance of an overall hit than with nose-mounted guns if the pilot's aim is off.

The British had the 8x .303 guns not harmonized called "The Dowding Spread" which was 12x8 feet at 750 feet. The reason was that they felt gunnery was poor (the ability of the pilot to hold the pepper on the target for over 2 seconds) was very poor. Non-harmonized guns have an overall greater dispersion so a greater chance of a hit for poor pilots but they will not concentrate. This can be a good decision for new pilots.

Some German FW-190 pilots did not use the wing-mounted 20mm guns because of the synchronization problem at close range and the 2x MG and 2x 20mm firing through the propeller was enough against enemy fighters. This saved weight too.

Nose-mounted guns concentrate their firepower for a "buzz saw effect" that wing guns cannot outside of their ideal harmonization range – if the aim is correct. However, if the pilot's aim is off all of the guns could miss completely. Nose-mounted guns firing through the propeller will have a slightly lower ROF (some state 10% to 40% lower) than wing-mounted guns. The P-38 did not have this problem.

The Corsair could have the two inboard wing guns harmonized at one range and one outer gun at another. The pilot had two triggers to fire one or both sets. This helped save ammo, and two .50cal guns hitting a Jap plane was enough to bring it down.

Occasionally, firepower effectiveness was measured experimentally. The Germans determined that a large sturdy bomber such as a B-17 or B-24 could be shot down with 20 hits of 20mm ammunition, three hits of 30mm HE ammunition, or one single 55mm hit. A fighter can be shot down with one 30mm hit, 3-5 20mm hits. The early war German 20mm MG FF gave a very poor performance for a 20mm round.

One way to determine damage is by firepower weight:
Hellcat, Corsair and P-51: six-.50 gunfire, throwing 9.4 lbs./sec. of lead per sec.

P-47: eight .50 gun fire, throwing 12.72 pounds of lead per sec.

P-38: four-.50 gunfire and 15 seconds of one (1) 20mm fire, throwing 9.22 lbs of lead per sec.

The P-38 has about the same weight as 6x .50cal gun but it will be concentrated and the 20mm HE will cause more damage.

The Allies' .50cal Armor-Piercing Incendiary round was a very effective penetrating armor at close ranges and starting fires.

As far as overall accuracy, most fighter guns had an average group of 4 mils, which is about 30 inches at 200 yards. So if your aim is on nose-mounted guns and wing guns hitting at their harmonized range will have a grouping of about 4-6 feet on the target IF the aim is on. If the aim is off enough it will completely miss.

Rather than a formula to determine the # of hits, you can use a formula to determine the % of the total firepower that hit the target and translate that into damage.

Then there is the problem of a 90-degree deflection shot. A plane moving at 200mph that is 30 feet long will only be in your line of fire for about 1/10 of a second. Firing 6x .50 cal guns will put out about 60 rounds per second. So no matter how many shots you fire you are looking at about a maximum of 6 hits.

If you are tailing and tracking a turning target you need to have a slightly greater turn rate to pull lead on the target to effectively get rounds on the target.

The bottom line is that it is not the accuracy of the guns but the pilot's ability to line up the shot long enough to put rounds on the target. In a maneuvering fight, it might be only 1-2 seconds or less. Some aircraft were better gun platforms than others too.

A good source is "Fighter Aircraft Performance of WW2
A Comparative Study" by Erik Pilawskii.

I hope that helps.

Wolfhag

For WW2 gun effectiveness this site is pretty good :

link

It has a corresponding site for modern aircraft guns:
link

Hope this helps,

B

You have dug yourself this hole by using the Spitfire as a datum, so there is no mathematical solution to your problem. I wouldn't worry as the rest of your equation is also essentially not fit for purpose from a mathematical standpoint. If it plays OK then don't ask yourself awkward questions.