From: Epijk@aol.com
Message-ID: <117.a94f233.296ba536@aol.com>
Date: Mon, 7 Jan 2002 20:28:22 EST
Subject: Re: Thrust and np
To: lancair.list@olsusa.com
MIME-Version: 1.0
Content-Type: text/plain; charset="US-ASCII"
Content-Transfer-Encoding: 7bit
Reply-To: lancair.list@olsusa.com

          <<<<<<<<<<<<<<<<--->>>>>>>>>>>>>>>>
          <<  Lancair Builders' Mail List  >>
          <<<<<<<<<<<<<<<<--->>>>>>>>>>>>>>>> 
>>
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AND, (with the exception of machinery which has miraculously rescinded the 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

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
LML website:   http://members.olsusa.com/mkaye/maillist.html
LML Builders' Bookstore:   http://www.buildersbooks.com/lancair
Please remember that purchases from the Builders' Bookstore
assist with the management of the LML.

Please send your photos and drawings to marvkaye@olsusa.com.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>