Hi Vip,
My quick formula sketched above was to show by the absurd that you can't boost anytime anywhere anyhow. In my example if P=0 (outside air pressure) there is no compression at all.
Secondly the compressor is actioned by the engine and such take a non-negligible power out of the engine for the compression of the intake air.
The higher you climb, the more the air need to be compressed but as the air is less dense the at a cte fuel/air mixture, the less fuel would be injected lowering the subsequent power available for the mechanical compression of the air.
This is why as you know Compressor are rated for a given alt.
Now let's get back to the higher octane fuel. Let says that the M engine (this is an example) give 8lb at 15000. As the engine need to be fed by more air at any given altitude to outsource the power of the higher graded fuel, at 15000 the compressor would hve run earlier (e-g at a lower alt) it's full potential.
Hence you max boost would hve been at 3000ft lower hence the max power wld hve been available at a denser air hence your max speed hve some chance to be less spectacular than with a slide rule (the ^3 effect of power/drag as you hve rclled us earlier - where drag means everything and not only external body drag)
SO it's more balanced that saying that if I hve got 100hp more out of an engine powering a giving airframe I would hve a top speed increased by 100/initial power * top speed of airframe
Ok Ok most of this you hev taken it into account. But what I mean is that only by changing the fuel, the SPit won't hve automatically a better top speed. Many thing hve to be adapted like the carb inlet (what you hev mentioned) or the pulley, the size of the compressor wheel (the volumetric ratio) etc... It is doubtfoul that BoB Spitfire where converted to the final standard due to historical events.
Yes the 100 wld hve had a better accel and this is confirmed by the combat report man can read (I am thinking abt that top leading ace that was shot down racing deck with spit in in 6 sure enough that he was safe in his faster 109 - need to dig out his name)
Material ?
to put it short : the amount of E of a system [du] equate somewhat the amount of caloric E (Q in joules) and the amount of work [dW] (1st thermodynamic low -
damn always forgot the right nbrs )
If you put in more internal U you also got more Q to get a slight amount of extra W (as it's easier for the E to be drawn out as extra Q than to be converted in more W). And don't forget that the more Q you had in any piping (I mean a closed syst) the more T is raising hence the more the viscous effect you hve to deal with (air then drag (see above))
Take for example the compound series of eng from the Germans with for example two 601 mated together on the same shaft . Did the output power was increased by a factor of two... no !
This was a silly example as well but it was meant to show by the extreme my purpose.
Here is what I mean : higher grade means higher strain on the eng (and I mean direct mechanical works too) with the consequence of a lower eng life. Yes engineer knew in 1940 how to pull out 2600Hp out of a merlin ... but for how long ? Would it fit any fighters pilot expectation ?
To drive
a comparaison with cars : I can pull 1000HP out of a Nissan Primera but would I out speed a Porshe ? (Plsd post it on Youtube
)
Sry this is a rather long post
~S