Warning: This gets into some hardcore calculations

 

In the course of dealing with a refueling issue, I did some measurements I would not normally have done. I obtained some results that may or may not make sense.

 

I sent an F/A-18D tanker cruising out from its base. Every time its "bingo" status dropped by 10%, I checked its distance to base (F6 in the group window) and fuel range remaining (F in the unit window). I expected that the distance traveled plus distance remaining would add up to a constant (1050 nm, the initial basic range of the plane).

 

What I found was that the two numbers added up to an increasing total, so that the plane was able to travel significantly further than 1050 nm total.

 

There is a certain amount of round-off error to these results, for several reasons. First, because the mouse must be moved around to get the information needed, my reaction time has an effect. Second, the game may not do the calculations continuously. There may be other reasons.

 

I used a land base to ensure that the base was in the center of the formation.

 

the measurements:

 

% above bingo distance to base fuel remaining total range

90 85 nm 983 nm 1068 nm

80 159 nm 927 nm 1086 nm

70 227 nm 875 nm 1102 nm

60 289 nm 829 nm 1118 nm

50 340 nm 790 nm 1130 nm

40 388 nm 754 nm 1142 nm

30 428 nm 724 nm 1152 nm

20 467 nm 694 nm 1161 nm

10 505 nm 666 nm 1171 nm

0 536 nm 642 nm 1178 nm

 

Since it is pretty simple to subtract the distance to base from the listed plane range, and the game is not doing that, there must be something else going on.

 

I have a guess, but it would be better for someone who knows what's going on to say so, rather than me making guesses.

 

a graphical representation

Warning: More hardcore calculations

 

It can be seen from the graph in the previous post that, for a plane traveling straight out from its base at a constant (cruise) speed,

 

1) The relationship between the distance to the base and the percent above bingo is almost linear;

2) The relationship between the fuel remaining and the percent above bingo is almost linear;

3) The sum of the fuel used and the fuel remaining is almost linear, but not constant.

 

I won't be considering point 3 immediately. I do have a possible explanation for it, relating to the physics of flight, although it would be good if someone who actually knows why this is happening just says so.

 

One of the curves is redundant, so I will discuss only point 1 here, and only in part.

 

I will ignore the non-linearity for now.

 

We know that, whenever you launch a plane, there is a quantity, which I will call Q, which is always equal to 1 at that time. It is stated as "100% bingo". We know that Q is equal to 0 (stated as "0% bingo") when the plane has reached a certain distance from its base, and that distance can be any value between zero and some maximum value.

 

We know that Q depends both on the distance to the base d and on the fuel available F. There often is a clear relationship between F and d, but this is not required.

 

When the plane is at bingo fuel (Q = 0) and tries to return to base, its remaining fuel is always more than the distance to the base. I don't know how this difference is calculated, but I am assuming that it is a fixed value for that plane. It may be something like the fuel required to loiter for half an hour. I am calling it the "bingo reserve" (BR).

 

There are 2 simple ways of constructing functions that meet the above requirements. One is a product of 2 terms, one linear in F, the other linear in d. The other is shown below.

 

Definitions

 

d: distance to base

F: fuel available

F_o: maximum fuel

BR: bingo reserve

 

Q = (F - d - BR) / (F_o - BR)

 

If Q is less than zero, it is set to zero.

 

The reason I am doing all this is that I want to know what the meaning of the "percent bingo" term is. Of course, it would be good if someone who actually knows just says so.