Daveroo,
An interesting question. Here's a couple of other formulas that might help.
Distance:
The mil radian formula won't help unles the plane is directly overhead. It works by changing your perception of the size of the object to an angular measurement, in this case mils. By knowing your target's size and then how may mils it appears, you can accurately determine its distance or alitude if above you.
It is: Size divided by mil(s) X 1000 equals distance or range or directly above, altitude
Examples:
A wing width of 40' / 20 mils = 2 X 1000 = 2,000' distance to the plane
If the plane was closer and took up say 40 mils it would look like this:
A wing width of 40' / 40 mils = 1 X 1000 = 1,000' distance to the plane
To properly use this formula, you will need binoculars or a scope with a milradian scale as well as know the size (height or width) of your target. If you remember the old submarine movies you will recognize this techique from the periscope view and the vertical and horizontal scales marked in 10s in the scope's reticle. Ships of various classes had known heights and lengths and by using the mil scale and formula, the skipper could determine the distance to the enemy ship. Of course ship angle and curvature of the earth would complicate the procedure. While a nautical description, you can see how it applies here.
Altitude:
To find altitude when the plane is at an angle from you, you can use trigonometry. you need to use the tangent of the angle of the aircraft above the ground and we also need to know the horizontal distance to our plane. What we are doing here is determining the ratio between two known sides of a triangle to determine the altiude of the third leg, in this case the aircraft's elevation or altitude.
Example:
Angle to aircraft of 20 degrees. Horizontal distance 5000'. height: Unknown
Tangent of 20 = 0.364 X 5000' = 1820' altitude
This will work well if you know the distance to the road or land feature that the plane is flying over. You can make a simple angle measuring device at home from carboard and a weighted string to determine angles. Some compasses have an angle scale built into them, but you don't see too many of them. Brunton used to make a compass that would measure angles and I just recently saw a Chinese military compass with the same feature.
Back in the days of anti-aircraft artillery, gunners often estimated altitude by firing shells until they detonated just below the clouds over their cannons. This would give the gunners a fairly good estimate of an attacking plane's altitude if it was near the cloud and a good guestimate or SWAG (scientific-wild-ass guess) if the plane was any distance below or above the cloud stratum. They could then set their fuzes accordingly.
