## A Problem with Spitfires

Posted in Cute Problems, History, The Universe and Stuff with tags , , , , , on July 25, 2017 by telescoper

This problem stems from an interesting exchange on Twitter last night, prompted by a tweet from the Reverend Richard Coles:

I think his clerical vocation may be responsible for the spelling mistake. The answer to his question doesn’t require any physics beyond GCSE but it does require data that I didn’t have access to last night.

Here’s a version for you to try at home with all the necessary numbers (though not necessarily in the right units):

A model of a Mark VI Spitfire showing its two 20mm cannons.

A Supermarine  Mark VI (Type 350) Spitfire fighter aircraft weighing 6740 lb is initially travelling at its top speed of 354 mph. The aircraft is armed with two Hispano-Suiza HS.404 20mm cannons, one on each wing, each of which is fed by a drum magazine containing 60 rounds. Each projectile  fired from  the cannon weighs 130 grams, the rate fire of each cannon is 700 rounds per minute and the muzzle velocity of each shell is 860 m/s.

(a) Calculate the reduction in the aircraft’s speed if the pilot fires both cannon simultaneously until the magazines are empty, if the pilot does nothing to compensate for the recoil. Express your answer in kilometres per hour.

(b) Calculate the average deceleration of the aircraft while the cannons are being fired, and express your result as a fraction of g, the acceleration due to gravity at the Earth’s surface which you can take to be 9.8 ms-2.

(c) A Mark 24 Spitfire – which is somewhat heavier than the Mark VI, at 9,900 lb (4,490 kg) – is armed with 4×20mm cannons, two on each wing. The inboard cannon on each wing has a magazine containing 175 rounds; the outboard one has 150 rounds to fire. Repeat the above  analysis for these new parameters and comment on your  answer.