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ELEMENTARYMECHANICS of
BOMBINGWhere the Bomb Drops-
How it Falls-and
4O00O,
ONE frequently hears the remark, "Thataeroplane must be about overhead bythe sound of it. Do you think we hadbetter go to the shelter? " To which somemote knowledgeable person replies, philosopic-ally, "Well, if he's right overhead, the bombsmust fall at least a mile away."This is fairly trueif the bombs are dropped .'-,/
at the instant of speaking. But if an aeroplane "is right overhead it may be that a bomb isjust about to arrive. It should be remembered that a bombcannot be heard at the time of its release, but only duringabout the last five seconds of its fall. So that when theaeroplane is right overhead, a bomb may have completedall except the last five seconds of its fall, and have beenon its way for 20 or 30 seconds, quite silently as far as weon the ground are concerned. Why it should arrive justabout when the aeroplane is overhead will be demonstratedby the laws of mechanics.A bomb is simply a body which is projected horizontallyat a height above the earthalthough its consequencesmay be far from simple. Its horizontal velocity at theinstant of release is that of the aeroplane which releases it.Its vertical velocity is zerothat is, if the bomber is doinga level bombing attack and not a dive attack. (Then.echanics a,s worked out here are only for the level attack,and do not apply in any way to dive bombing.)The vertical velocity increases rapidly under the influenceof the acceleration due to gravity, so that the trajectoryis a curved path of increasing steepness. The accelerationdue to gravity is approximately 32ft. per sec. per sec, sothat after two seconds the bomb is travelling downward atthe rate of 64ft. per sec. This statement must be qualifiedslightly by saying that this would be its speed if there wereno air resistance; and, if this were so, its horizontalvelocity would be always equal to the bomber's speed atthe instant of release. The series of curves which havebeen drawn in the chart are based on the assumption ofno air resistance. They give data for bombs falling in a
vacuum, and have been drawn for different heights anddifferent forward speeds of the bomber.Effect of Air Resistance
The effect of air resistance is two-fold. It prevents thevertical speed increasing at such a great rate as it wouldin a vacuum, and also sets a maximum to it. That is tosay, the bomb goes faster and faster until it reaches whatis called its "terminal velocity," or T.V., and after thatdoes not increase in speed.It should be realised that the curves drawn are theo-retical in that they neglect the very important air resist-ance. But data on actual trajectories cannot be used owingto censorship, and, in fact, such information is jealouslyguarded by the authorities who do the scientific work to(btain it. (On the figure is shown a dotted line marked"Actual trajectory"; this has no quantitative meaning;at all, and is merely intended to show that the bomb woulddrop more steeply than the theoretical path.)Actual trajectories can be calculated, but it is a veryinvolved mathematical process. If the air resistance of abomb at a certain speed is known (and this can be deter-mined in the wind tunnel), its resistance at all other speeds"an be calculated. Variation of air density with height is
Acrual trajectory from 200m.p.hbomber issrwper rhm parh invacuum.
Z 3 4 5 4 9 ? l 0 9 2HORIZONTAL FLIGHT OF BOMB (inmilts)
Data on the tracks ot projectiles without air resistance.known, so at all points of its fall, the two forces acting onthe bomb, the attraction of the earth and the air resist-ance, are known, and its speed and path can be workedoutbut not by ordinary mathematics. It may involveadopting an exponential law for the variation of density,using Siacci's tables for the air-resistance function and in-tegrating the equation of motion by Picone's method.
The second effect of air resistance is to reduce the hori-zontal velocity. If there were no air resistance, this wouldremain constant at its initial value, and if the bomb weredropped from an aeroplane travelling at 200 m.p.h. it wouldstill have a horizontal velocity of 200 m.p.h.combined,of course, with its vertical velocitywhen it hit the ground,no matter from what altitude it had been dropped. Butair resistance gradually reduces this, and if the fall of thebomb continues for long enough its horizontal velocitybecomes zero, and it will drop vertically.Terminal Velocity
By this time it may also have reached its "terminalvelocity," and its flight path will then be a vertical straightline with its speed constant. If it may be assumed thatthese bombs which are being dropped from 20,000 andmore feet have reached a steady downward speed, someidea Of the value of the T.V. may be obtained. Everyoneknows that they hear the whsszswhszzzss of the bombbefore it arrives ; this indicates that it is then travelling atless than the speed of sound, which is about 750 m.p.h. atsea level.The chart shows that the vertical velocity of a bombdropped from 20,000ft. in a vacuum would be the tre-mendous value of 773 m.p.h. (This figure applies to anypiece of matter ; even a feather released at this height ina perfect vacuum would hit the ground at 773 m.p.h.and would probably penetrate it. But the problem ofcreating a perfect vacuum from the ground up to 20,000ft.would make the heart of the most ingenious scientist quail,so there is no need to worry over the prospect of beingbombarded with feathers at 773 m.p.h. even in this mostmodern of wars.)Approaching the speed question from the other way, weknow that the terminal velocity of a streamlined modernmonoplane is something like 500 or 600 m.p.h. Its shapecorresponds somewhat to a bomb with wings, so it is likelythat the terminal velocity of the bomb, having no wings,will be somewhat higher. It must be remembered, how-ever, that the surface roughness of the bomb is greaterthan that of the aeroplane, and this will cause considerableresistance at high speed. So it is likely that the T.V. ofa bomb is in the 550 to 650 m.p.h. range.The actual time to fall is greater than the theoreticalfigure worked out for no air resistance. So from 20,000ft.the time is considerable, being over 35 seconds. But it can-
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E L E M E N T A R Y M E C H A N I C S O F B O M B I N G ( C O N T I N U E D )not be heard all this time because any sound made at greatheights is simply damped out and lost. One cannot heara whistling noise from a distance of three or more miles.In this time the bomb covers a considerable horizontaldistance, depending on the speed of the bomber. For20,000ft. and 200 m.p.h. the theoretical distance is 1.95miles. Air resistance would reduce this somewhat.If the bomber continues in straight flight after droppingits bomb, it will remain always vertically over the bombtheoreticallysince the bomb continues to move horizon-tally with the same speed as the bomber. Hence the state-ment made in the-second paragraph that if an aeroplane isOverhead it may be that a bomb is just about to arrive.Actually, the effect of air resistance is to make the hori-zontal position of the bomb lag slightly behind that of thebomber. The dotted aeroplane on the chart shows thebomber position a short time after dropping its bomb. Thetheoretical position of the bomb is found by dropping avertical line down to cut the trajectory marked with theappropriate bomber speed, which in this case has beentaken to be 200 m.p.h . If the dotted curve represented areal trajectory, then the aeroplane would be the distanceAB ahead of the position where the bomb hit, for a bomb-ing height of 20,000ft.The angle at which the bomb strikes, or the angle ofimpact, cannot be obtained from this chart, as the ordi-nates are not to the same scale, the horizontal being tonearly twice the scale of the vertical for easy reading. Ifthey were done to the same scale, the angle of impact couldbe obtained simply by drawing the tangent at the appro-
priate height on the line of appropriate speed. It is obviousthat increase of speed and decrease of altitude both tend toflatten the impact angle.Dive Bombing
Dive bombing is a type of attack with entirely differentcharacteristics from level bombing. In this the aeroplaneis put into a steep dive, and is itself aimed at the target.The bomb is released at low altitude, after which the aero-plane is pulled out of the dive. The whole manoeuvre isa very severe one on the pilot, as the dive subjects him tosudden atmospheric pressure changes, and the subsequentpull-out to a high value of acceleration which imposesterrific structural loads on his body and on the aeroplane.It will be realised that the steeper the dive, the greateris the probable accuracy. Th at this is so is evident froma vertical dive attack. In this the trajectory would be avertical straight line, and would not be curved by the actionof grav ity. Therefore, it only requires the correct aimingof the bomber before release of the bomb to ensure a hit.Also, the vertical speed of the bomb is greater, the steeperthe angle of dive, and in the vertical dive the maximumimpact speed and impact angle, 90 deg., are both obtained.For these reasons vertical dive attacks seem as though theymight be very effective, but the physical stresses on thepilot and aeroplane are both increased tremendously, andsuper varieties of both would be required. It seems likelythat dive bombing will be restricted for the present toangles of something like 50 deg. And it is only a com-pletely reckless pilct who will dive into a balloon barrage.DESIGN TRENDS' "THERE is a definite trend to greater gross weight foreach type of military aeroplane, due mainly to re-
quirements for increased performance, which have called forlarger and heavier power plants. The overall size of ourstandard types remains about the same, due to increasingcompactness of design.The trend to greater speeds continues, increases inspeed being attained through aerodynamic refinement andincreased power.Present effort in aerodynamic refinement is to achievevery smooth surfaces and true contours, and to eliminateall gaps and air leakages.Increased wing loadings and improved high-lift devicesare inevita ble. Assisted take-offs for certain types are apossibility.There is promise of achieving laminar flow over a largeportion of the wing, with consequent large reduction in
'wing drag. This line of development points to pusher-propeller installations.Compressibility shock is becoming an imminentproblem . Different wing sections and different fuselageshapes are being evolved to avoid compressibility effect.This effect indicates that maximum speed will be attainednear sea level.There will be increased' use of stainless steel, mag-nesium, and plastic materials.Superchargers are undergoing intensive development.Fuel in quantity of better than 100 octane rating can beexpected soon. The trend to drive propellers through ex-tension shafting has brought forth new power-plantproblems.The Present Trend in Design and Size of MilitaryAircraft (digest) (B. K. Yount, J .S.A.E., Vol. 47, No. 2,Aug., 1940, p. 25).
ORIGINAL THEME WITH VARIATION. TwoSkuas and a Roc of the Fleet Air Arm. Thelatter has a Boulton-Paul turret.
