Friday Official Update, July 20, 2012

[MD_Marx]

Originally Posted by Wolf_Rider

Determine the weight of the falling object. The easiest way to do this is usually to measure this quantity directly. You can also estimate weight if you know the construction materials and dimensions.

2
Calculate the frontal area of the falling object. The frontal area is the apparent area facing in the direction of falling. You can determine this area by measuring the outline of the object from that orientation. For example, if the falling object were a cone, the tip of the cone would point straight downward, and the frontal area would appear to be a circle equal to the area of the circular base of the cone.

3
Determine the drag coefficient of the falling object. You can usually avoid having to calculate the drag coefficient yourself by looking up an approximate value in a reference book or on the Internet. If you need a highly precise value, you should consult with an engineer.

4
Determine the gas density of the medium through which the object will be falling. If the medium is the air, then you should know that air density decreases with altitude, which means that the object's terminal velocity will decrease as it gets closer to the ground (where the gas is denser and pushes back harder, providing stronger braking power). Thus you can calculate terminal velocity at any one altitude using simple mathematics, but to calculate the change in the terminal velocity over a long-distance fall, you will require the use of calculus or empirical approximations. Air density also changes with the weather; there is no uniform density value for a given altitude. To get the most accurate measurements of air density, you will need to multiply average air density values by local weather condition offsets. Atmospheric information is available in the United States from the National Weather Service, a service of the National Oceanic and Atmospheric Administration.

5
Calculate terminal velocity at a given altitude with this equation: Terminal V = sqrt ((2 x (Object Weight)) / ((Frontal Area) x (Drag Coeff.) x (Gas Density))).

In plain English, the terminal velocity of the object is equal to the square root of the quotient of twice the object's weight over the product of the object's frontal area, its drag coefficient, and the gas density of the medium through which the object is falling.



Read more: How to Calculate Terminal Velocity | eHow.com http://www.ehow.com/how_6134922_calc...#ixzz21SPSlnUQ

Thanks for this very interesting item - I haven't looked at the article yet, but you might need to consider a few more variables before identifying a value for Cd for the bomb.

1. Bombing altitude. If you are bombing below the height needed to attain terminal velocity, the bomb won't attain it, and the Cd value will need to be computed from a theoretical velocity.

2. The Cd of falling objects will generally increase to a point where the object has shock waves generated from it at near-sonic bomb velocities. As the bomb goes sonic/trans-sonic the Cd will probably drop slightly.

3. The Germans did an awful lot of aerodynamic research during the war, and I would be surprised if the likes of Schlichting et al did not provide a pretty comprehensive Cd-Velocity envelope for specific bombs, or a more generic CD-velocity profile for use in general calculations?

4. My own interest in this has been from determining the theoretical 'effective' range of WW2 aircraft cannon/mg, in which the highest velocity (and drag) is established at the muzzle and thereafter decays through sub-sonic drag. For my calculations, I found a very interesting article on the net by a team of Indian researchers who managed to investigate and tabulate the trans & sub-sonic CD values of a fired test cannon shell. I appreciate that the bomb is probably more aerodynamic than the shell, but the CD - Velocity characteristic will be similar.

5. Air density - or static pressure - is generally a function of altitiude but of course changes due to atmospheric conditions. If my memory serves, air density can be calculated from P/RT where P is the pressure at altitude (which will vary as the bomb descends), the gas constant R for air and the absolute temperature. No-one can predict precise values from the (discomfort) of a bomb-sight, but these values should be reasonably accurate.

Hopefully I can now take off my annorak, as it's getting rather warm in the UK

Marx

[TomcatViP]

Originally Posted by MD_Marx

As the bomb goes sonic/trans-sonic the Cd will probably drop slightly.

[...]

my annorak, as it's getting rather warm in the UK

Marx

Wait wait... transonic drag is much higher than subsonic. This why it is called the Mach wall.

[Wolf_Rider]

Originally Posted by MD_Marx

Thanks for this very interesting item - I haven't looked at the article yet, but you might need to consider a few more variables before identifying a value for Cd for the bomb.

1. Bombing altitude. If you are bombing below the height needed to attain terminal velocity, the bomb won't attain it, and the Cd value will need to be computed from a theoretical velocity.

Though I didn't write that up, it does suggest that the calculations required are not a simple feat

and I guess that's why (the yanks, at least, in the later stages and the PTO) went back to iron sight "guestimating" , dive and skip bombing for low level raids?