my maths not guaranteed...
Odd but true. Is it not the case that the art of the jet is to fly fast enough to increase L/D dramatically? The jet at a mere 365ktas obtains for the sake of argument an L/D of 14.5 and burns 0.65lb of fuel per hour per pound of thrust. So if the jet weighs, shall we say again, 34500lb it will cover 240nm per 1000lb of fuel according to Breguet’s formula. A turboprop having the same weight will also cover 240nm per 1000lb of fuel providing that the following stipulations are met. Firstly actual speed in ktas is not specified but is derived from the necessity of maintaining an identical L/D ratio, in this case 14.5. Secondly the ratio of propeller power efficiency to fuel consumption in lbs per horsepower hour must be 1.75:1, which is easily met, say 85% and 0.486lb/bhp-hr typical of the PWC 120A in cruise. The jet Breguet formula gives nm = (V/c)*(L/D)*ln(W1/W2); slightly differently the prop Breguet formula gives nm/lb = 325.65*(e/c)*(L/D)*(1/W). I know that the former is a range and the latter is a range per pound of fuel but only the former explicitly states speed. Also yup the jet sfc is lb/lb-hr and the prop sfc is lb/hp-hr but equating nm at speed V and nm/lb for the same L/D is an easy mathematical problem. With the prop you have to derive speed from the requirement that L/D must have a specified value. But the prop craft finds it harder and harder to improve L/D because the faster it goes the worse becomes its prop efficiency “e” unless it has a very high wing with very long undercart legs to accommodate a very big prop which gets lossy anyway due to the blade tip speed. So by this example at 365ktas the two types are equal in terms of fuel consumption but not speed. The prop is flat-out Charlie but the jet has speed in hand. Should the jet increase speed its L/D gets better and should it climb higher its drag gets lower. To match it the prop can only fly faster and its propeller efficiency gets worse defeating both objects of the game to fly faster and get higher. Meanwhile the jet consumes much the same in lb/hr for each pound of thrust. So the prop cannot fly fast enough nor high enough to compete in the L/D war but is much, much more fun. Not only back every afternoon but back several times in the afternoon! Aaaahhh, I’m getting old and loving it!