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In a message dated 1/6/2002 4:45:12 AM Pacific Standard Time,
StarAerospace@aol.com (Eric Ahlstrom) writes:
<<<...Thrust from a propeller is inversely proportional to velocity:
T = 550 * np * HP / V ...>>>
Here, you state the obvious as if it were a great revelation.
<<<...This has not been mentioned anywhere in these comments on tip speed...>>
>
You might note that in the comments to which you refer, which used tip mach
merely as a thumbnail indicator of propeller operating regime, the usefulness
of stating an obvious relationship (implicit to the whole discussion) seemed
quite superfluous.
<<<...I have to wonder where this idea of "percentage" came into use
regarding the propeller efficiency factor "np"...>>>
Well, let's try to make it clearer for you.
Rearranging your equation to solve for "np" produces:
np = (Thrust x Velocity) / (HP x 550)
(thrust in LBF, Velocity in FT/SEC)
>From that statement of the equation, it is obvious that what you call "np"
is no more than the ratio of "power produced by a propeller" to
"power input to the propeller". (Thrust x Velocity is power produced, having
units of FT-LBF/SEC; HP x 550 is power input, also having units of
FT-LBF/SEC).
AND, (with the exception of machinery which has miraculously rescinded the
principle of the conservation of energy) that number (np) is usually a number
less than one, often referred to as a "decimal fraction".
A long, long time ago, in order to relieve the arithmetically challenged from
the stress of working with decimal fractions, some clever guy invented the
concept "percent", which means "the number of parts per hundred".
I think it was somewhere back in fifth grade that someone told me that if I
wanted to do a calculation with a number expressed as a "percentage", then I
should divide the "percentage" by 100, then I could just use it like a plain
old decimal fraction.
Conversely, if I had a number like "propeller efficiency = 0.85", then I
could quickly do the "x 100" in my head and call that 85%. Isn't that slick?
(BTW, it also works for numbers bigger than 1.0 !!!)
Ever heard the thermal efficiency of a piston engine expressed as 28% (or 31%
or whatever)? Same concept: energy extracted off the crankshaft divided by
energy content of the fuel burned to get it, x 100 to get %.
<<<..."np" is ... represented by the product of the advance ratio (J)
multiplied by the ratio of thrust vs. power coefficients...>>>
Yes, that's ONE of the definitions, but another, equally valid one is:
np = (Thrust x Velocity) / (HP x 550)
If you need verification of that definition, you can check any number or
engineering texts. One of the best is: AIRCRAFT DESIGN: A CONCEPTUAL
APPROACH, by Daniel P. Raymer. Another one (simpler) is AERODYNAMICS FOR
NAVAL AVIATORS.
<<<..."np" is a dimensionless number ...>>>
I'll bet you already figured out that PERCENTAGE is a dimensionless number
too.
<<<...np = the efficiency factor .... of the prop at that particular
flight condition (this changes with velocity, advance ratio, tip speed mach
limit and many other factors)...>>>
Very good. And the three-dimensional matrix characterizing the performance of
a particular propeller throughout it's operating range can be composed from a
series of two dimensional matrices which, for different altitudes, state np
values at each intersection of specific J (advance ratio, typically abcissa)
and power loading (typically ordinate) values. (I have many of these maps,
both from Hartzell and from MT, if you'd like to see one for real.)
<<<...Useable tip Mach and "np" varies considerably with prop type and
technology.
Thick wood props with (archaic, but still used) Clark Y airfoils have very
low useable tip Mach, some as low as .75. Some (not all) composite and
aluminum props with thin, swept, supercritical sections can achieve greater
than .85 np at tip Mach of .91 to .94...>>>
Agreed, but none of that changes the basic statements in the referenced post
regarding the typical peak efficiency numbers actually achieved in service by
"normal" $15,000-and-below props (Note that no one made any reference to
supercritical sections, scimitar props, or the like. I know Hartzell {and
probably others} have them available, but it didn't seem to me, reading
between the lines, that Mr. Casey had one of them in mind. I could be wrong)
<<<..."Propulsion efficiency" is the more comprehensive factor that
represents the
actual net thrust minus all the losses (aerodynamic, cooling, etc.) that
don't get counted in the basic HP vs. T equation. Yes, thrust causes drag;
not just because we are going faster, but also because the greater thrust
impinges on the airframe more and the greater HP creates more heat that costs
us more drag to get rid of. All of these things are recorded by the
aerodynamicist as "negative thrust" and constitute the difference between
"uninstalled" (books, dynos, prop charts) and "installed" thrust. Increasing
Peff often has a better return on investment than beating on the engine or
prop for more efficiency...>>>
I'm not sure, but I think all that bla bla bla can be reduced to:
"In steady-state (unaccelerated) flight, net thrust = total drag."
<<<...HP = brake horsepower imparted to the propeller, SAE net for all you
gear
heads...>>>
Thank you for putting it into terms we can all understand.
<<<...Time to toot my own horn here, we do this for a living...>>>
Interesting. Is obfuscation billed by the hour or by the job?
((BTW, aren't you the guy who asserted, not long ago, that "...the PSRU's on
all turboprop engines relied on helical gearing..." ?? Seem to remember that
being rather convincingly refuted.))
Jack Kane
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