An excellent and praise-worthy post from
bookworm, whose post should put to rest queries fom those who wondered at the origin of the 1.32 'rule' for the
theoetical jet transpot.
Bookworm has qualified his/her response well, adding 2 very significant 'it all depends' caveats with the last two notes.
I'd like to add a further consideration for the jet transport, and that is consideration for wave drag (the High Speed Polars) for flight above Mcrit.
Bookworm has specified (correctly) that "
D = V^2 + 1/V^2 (parasite drag + induced drag)", fine for flight below Mcrit (typically at altitudes below typical jet cruising levels), but at levels where 1.32 Vmd is above Mcrit, a third component for Total Drag must be considered, where -
Total Drag = Parasite drag + Induced drag + Wave drag.
An approximation for Wave Drag for a
generic and theoretical jet is (V - Vmcrit)^3, thus the Total Drag (theoretical) is best summarised as -
D = V^2 + 1/V^2 + (V - Vmcrit)^3.......... (Which accounts for relatively small wave drag increments for a short time above Mcrit, but increasing substantially thereafter).
After applying calculus to find the Maxima and minima after this third drag component is considered, it inevitably leads to Speed for Maximum Range being
BELOW 1.32 Vmd, and significantly below at higher altitudes.
99% of Jet operations are above the level where Mcrit comes into play, with Max Range Speed inevitably just above Mcrit. Thus, whilst the 1.32 Vmd 'rule' is a good approximation at lower levels, it becomes redundant at typical cruise levels for jet aircraft.
I am definately
NOT criticising
bookworm's excellent (and well qualified) post, I am ADDING to it.
Regards,
Old Smokey