My first order calculation considered only the action-reaction principle, and assumed no energy sinks such as recoil damping mechanisms or, perhaps important here, INDUCEMENT OF DRAG.
Putting the plane at lower speed, and requiring to pitch up a bit for aiming so as to lob in those shells from longer range, imply a not insignificant angle of attack. If the angle of attack were to be increased slightly more by the recoil, that could well lead to an additional velocity decrease via additional induced drag. Not to mention if the pilot is executing some amount of 'porpoising' in pitch during this exercise.
Going back to basics, and invoking the physicist's favourite apparatus, the notional frictionless and massless sled, we can imagine a B-25 placed on such a sled and determining the recoil velocity. The simple reciprocity formula applies if the gun's barrel is in the plane of the surface upon which sled slides, AND all recoil energy is transferred to the plane as an essentially rigid structure. We can take the gun barrel to be sufficiently aligned with the plane's longitudinal axis that any vector component of velocity out of plane to be quite negligible.
Earlier I used a simple mass ratio of shell : plane of 1 : 1,000 for simplicity of calculation. If you know the actual masses and the shell's muzzle velocity, the same reciprocity principle applies. For instance, if the mass ratio is 1,685, the recoil velocity upon the plane is the muzzle velocity/1,685.
Inducement of recoil is an acceleration, occurring over the interval of the shell's acceleration through the barrel. It's brief enough to be sensed as essentially violently instantaneous. And so for our purposes we can consider recoil to be an instant application of velocity. If this kick were to be 1m/s, the plane on our sled will slide rearward at this speed, gradually slowing down to a stop due to air friction after some period of time.
If our plane, on its frictionless sled, is sliding down a slight decline of slope such that air friction imparts some particular terminal velocity, the recoil will instantly subtract from that velocity, after which the plane will speed back up to its former terminal velocity. This is akin to a plane in (more or less level) flight under application of continuous, fixed power. The higher the velocity, the greater the air friction and hence the longer the interval to regain a given speed lost to recoil. (The velocity curve of a body to friction-induced, terminal speed is somewhat asymptotic, meaning the rate of velocity change continually decreases as the terminal velocity is approached.)
It might bear on the matter to consider the component of recoil contributed by the propellant gas. To first order we take the powder mass and assign it some average velocity during the shell acceleration. Upon the shell's escape the gas rapidly evacuates and expands, dissipating a good fraction of its energy and thus probably imparting only a small additional component to recoil. Or maybe we could apply something of a best case scenario and simply treat the propellant like the shell, adding the two masses together and exiting at the muzzle velocity.
Anyway, just some useless musings on a slow spell to recharge between bouts of modding.
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Topic: B-25 with 75 mm gun vs ships (Read 854 times)
