I have been giving some thought to the time of fall of conventional ballstic “iron” bombs.
Crucial to this is the “terminal velocity” of the particular type of bomb.
I understand that the human body’s terminal velocity is generally around 100-120 mph. Of course bombs are usually somewhat more aerodynamically shaped and thus will have less drag and have a higher terminal velocity.
Their initial horizontal velocity will be that of the aircraft but that will reduce as drag slows it’s forward velocity down. We can assume (for the sake of this discussion only) that the aircraft is flying straight and level so the initial vertical velocity is zero. It will of course accelerate downwards under gravity at an acceleration of 32 ft/sec/sec until it reaches its terminal velocity.
Maybe partially relevant is that most bombs are released in a horizontal attitude not the near vertical attitude of their fall. However they actually fall in a sort of curved/parabolic path in the vertical plane. That path will be also curved/parabolic in the azimuth plane as well due to the effect of wind on both the releasing aircraft and upon the weapon itself.
But what is that terminal velocity? AP1730A shows an example levelling card which appears to indicate that T.V.s vary from 1,000 ft/sec to 2,820 ft/sec. Which I make as 681 to 1,922 mph! Thus it seems that bombs are mostly supersonic not subsonic and yet the films will have us believe that falling bombs make a whistling sound. (Apart of course from the supersonic V2 rocket.)
Now using those well known schoolboy equations of motion v=u+at, s=ut+½at2 and v²=u²+2as it should be possible to do a basic calculation of distance and time to fall to reach TV and then time to fall the remaining height to ground level. Which is OK if one believes those TV speeds.
The TV setting knob on the MkXIV/T-1 computors was replaced, in the T-3 and T-4 computors, by a “ballistics allowance” scale calibrated in degrees of rotation (of a cam) rather than speeds. Perhaps because of the evident conflict of basic theory and actualities?
Can anyone shed any light on terminal velocities and time of fall?
By: masr - 30th August 2015 at 04:58
All that rather throws into perspective just how difficult it must have been in the early days of WW2 to hit a precise target.
Mike
By: Flying_Pencil - 28th August 2015 at 19:21
Thank you abadonna and aircraft clocks for your data.
Flight magazine on October 3, 1940 has an article worth reading and I include an extract:
“Actual trajectories can be calculated, but it is a very involved mathematical process. If the air resistance of a bomb at a certain speed is known (and this can be determined in the wind tunnel), its resistance at all other speeds can be calculated. Variation of air density with height is known, so at all points of its fall, the two forces acting on the bomb, the attraction of the earth and the air resistance, are known, and its speed and path can be worked out—but not by ordinary mathematics. It may involve adopting an exponential law for the variation of density using Siacsi’s tables for the air-resistance function and integrating the equation of motion by picone’s method.”
A bit beyond me!
Rocket science, but in reverse! :p
Excellent subject to bring up! One may hear the whistle from bombs that fell earlier, but not the one that falls on you!
By: TerryP - 28th August 2015 at 15:02
Thank you abadonna and aircraft clocks for your data.
Flight magazine on October 3, 1940 has an article worth reading and I include an extract:
“Actual trajectories can be calculated, but it is a very involved mathematical process. If the air resistance of a bomb at a certain speed is known (and this can be determined in the wind tunnel), its resistance at all other speeds can be calculated. Variation of air density with height is known, so at all points of its fall, the two forces acting on the bomb, the attraction of the earth and the air resistance, are known, and its speed and path can be worked out—but not by ordinary mathematics. It may involve adopting an exponential law for the variation of density using Siacsi’s tables for the air-resistance function and integrating the equation of motion by picone’s method.”
A bit beyond me!
By: aircraftclocks - 28th August 2015 at 14:23
Just reading a WWI document about bomb dropping theory and the following information was offered.
Group I., terminal velocity, 900 feet per second:-
16 lb., 50 lb., 63 lb., 100 lb., 112 lb., 520 lb.
Group II., terminal velocity, 1500 feet per second:-
180 lb., 250 lb., 550 lb.
By: abadonna - 28th August 2015 at 13:46
1,000lb Mk.6 with No.100 tail. (Note the Mk.6 was a high-speed/high-altitude bomb, so probably aerodynamically cleaner than a 500lb bomb). Release height 35,000ft/220mph TAS, trail 1,185ft, time of fall 49.15sec, air range 14,664ft, striking velocity 1195f/s. Release height 20,000ft/220mph TAS, trail 361ft, time of fall 35.81secs, air range 11,190ft, striking velocity 1,110f/s
By: TerryP - 27th August 2015 at 19:29
See Wikipedia: https://en.wikipedia.org/wiki/Bombsight#CITEREFBombing1944
So it seems an example is that; A 500 lb bomb dropped at 200 mph from 20,000 ft in a 25 mph wind travels 6,500 ft forward before impact with a cross trail caused by the wind of approx 1000 ft, arriving with a velocity of 1150 fps at an angle of about 77 degrees from horizontal in a time of fall of about 37 seconds.
Any other examples of velocity and time of fall would be interesting to hear.
By: Archer - 27th August 2015 at 14:51
An interesting subject. Something that is missing from the data is the altitude at which the load is released and the atmospheric parameters. Why? Because the drag changes with the density of the air. As the object moves downward through the atmosphere the terminal velocity will decrease because of the increasing air density. Approx 1% per 520 feet (source: wikipedia).
Terminal velocity is reached when the drag produced by the object and the gravitational pull on the object are in balance. But as the drag changes as a product of density, this number will change throughout the object’s travel downwards. Something to think about…. There are some hints on this page: https://en.wikipedia.org/wiki/Terminal_velocity
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August 27, 2015 at 11:17 am