Hi mate.
First of all: my sincere thanks by your explanation about the parabolic motion... but I know the works of sir I. Newton also.
BTW, I must point out an error in your eq. 3. It must be written as:
R = v . SQRT (2h/g)
Basically we are talking about of 2 types of bombsight: the Norden/Lofte type(Allies/Germans), and the OKPB-1 type (Russians). Both need 2 settings: TAS (horizontal speed), and altitude. The difference between both types is the first allows automatic or manual release, and the second only allows manual release. But in both types normally the aiming angle is internally calculated (all that equations you've posted run behind the scene).
The exception is the Norden/Lofte type when a player prefers the manual release; if so, he will must perform those calculations by himself (some players made an published their charts for manual release with the Norden/Lofte type, long before the patch 4.10).
According to my tests carried out several weeks ago, it seems that all bombs have the same FM, regardless of size and country (IRL the bombs' shape and weight are relevant, as well as the launching altitude, GS, OAT, and the wind's speed & direction).
As far as I can remember, when the atmosphere model had one only air temperature, the parabolic motion was almost perfect and it was very easy to adjust and to aim the bombsight, and to hit an intended target.
But now we have an atmosphere with different OATs at SL which change with the altitude, thus changing the air density dinamically.
I.e.: according to the AIS, if the OAT at SL is 25 ºC, we'll have:
Altitude (m)___OAT (ºC)___Air density (kg/m3)
0____________25_________1.225__(1.225)
1000_________18.5_______1.115__(1.088 )
2000_________12_________1.013__(0.966)
3000_________5.5________0.919__(0.858 )
4000_________-1_________0.831__(0.762)
5000_________-7.5_______0.75___(0.676)
6000_________-14________0.675__(0.601)
7000_________-20.5______0.606__(0.533)
* (The values into brackets are the air density at different altitudes considering a constant OAT = 0 ºC).
We could supose that any bomb released from a given altitude (say 6000 m), when t = 0, will have a constant horizontal velocity
v = TAS (a/c), and an increasing vertical velocity
u which range from 0 up to its final value. But both velocities will change with air densitý as the bomb is falling. Therefore, its path will not be perfectly parabolic as we could expect in a 'Newtonian Universe'.
Perhaps all bombs have the same in-game's FM... but they might work in a different fashion than that known before the patch 4.11.
Another factor which produce offsets between the aiming point and the hit point is how leveled flies the aircraft. If the pilot flies with the Level Stabilizer engaged, the aircraft may be flying at a steady altitude... but if its elevator is trimmed to avoid the 'sinking', probably its Angle of Attack (AoA) is not 0. The pilot will not be noticed about how is the AoA (the pitch), because the artificial horizon doesn't work when the LS is on, and because we haven't an 'AoA gauge' like the modern aircrafts have.
Thus, with that configuration, when the bombsite is at 0 º elevation, really it will be aiming at 'AoA' elevation.
I.e.: if the AoA is +3º, this angle adds to the bombsight elevation. A bombardier aiming to a target with a BS elevation = 50º, really is like if he would be setting an elevation of 53º, and then he adjusts the TAS and/or altitude to fix the target under his crosshair according to that wrong angle... which will worsen the final outcome.
A difference of 3º may seem a small thing; but if we make same calculations according to the equations you've posted:
Wrong elevation = 53º (the bombardier believes the elevation is 50º)
tan (53º) =
1.327
Right elevation = 50º (if the aircraft would be flying perfectly leveled)
tan (50º) =
1.192
According to your eq 7,
D(53) = 5000 x 1.327 =
6635 m
D(50) = 5000 x 1.192 =
5960 m
As you know, the most of players engage the Auto Release when the elevation is about 50º. Even if the crosshair is fixed over the target (what would be rare in this case), the bombs will fall about 675 m short because of the early release.
...
Other unavoidable errors related with the type Lofte/Norden BS:
This bombsite has not a 'coarse/fine' setting, but one only mode with 2 fixed rates: one for the TAS and the other for the altitude. The rate for altitude is 50 per keystroke, and that for TAS = 10 per keystroke.
But, depending on the chosen bomber, we have the following combinations:
- German bombers: TAS rate = 10 km/h; altitude rate = 50 m.
- Allied bombers: TAS rate = 10 KTS; altitude rate = 50 ft.
- Japanese bombers: TAS rate = 10 KTS; altitude rate = 50 m.
Thus, 1 keystroke of TAS in an Allied bomber BS is almost equivalent to 2 keystrokes in a German bomber; and conversely, 1 keystroke of altitude in an German bomber BS is almost equivalent to almost 3 keystrokes in an Allied bomber.
In short: German bombers allow more accurate TAS settings than the Allied, but the latter allow more accurate altitude settings than the German.
Other errors come from the instrument readings: sometimes the pilot visually must interpolate between two marks, and can be difficult to decide if he's reading a value of 12,600, or 12,700, or 12,800...
I'm wanting to emphasize that, even if the calculations were very accurate, the game interface makes it impossible to apply them exactly.
...
This evening I'll try to perform more tests, as you've suggested: one with a Russian bomber, and other with a German bomber at least.
See you later!
