Elon,
Ah! Yes, you are correct. As some of this stuff is starting to come back,
drag is the square of the speed, and power is the cube. The more power, the
faster the acceleration.
In a frictionless environment, a very small amount of power would
*eventually* get you up to speed, more power would just get you there
faster.
As you indicate, air resistance builds as the square of speed. I seem to
recall that all of the other frictions remain fairly constant. So, if you
know the air resistance of a vehicle, you can plot power against speed and
determine where horsepower equals air resistance (less the built in other
frictions, rolling resistance, bearings, etc., but I recall that these will
be very small compared to the air resistance) and determine your 'terminal'
velocity.
Since the track at Bonneville is of fixed length, I also seem to remember
working out that with a small amount of power, even though you had a very
slippery vehicle, you would not have enough time to reach top speed before
you ran out of road (because your acceleration would be so slow - this
sounds like a basic argument for a transmission. A 15 to 1 gear ratio
doesn't give me 15 times more horsepower - but it does give me roughly 15
times more torque(?) Or is it just a mechanism to allow me to couple the
best power producing setting on my engine to the current speed/acceleration
need?) <<It might be a good idea to sit down and think about this awhile
before blurbing out these emails>>
As far as the Reynolds numbers went (and I'm still reading some of the links
kindly provided by this forum), they indicated the slippery-ness or part of
the calculations for the air resistance of the body. The math around
calculating the airflow around any but the simplest of bodies was daunting,
and I recall my professor telling me, "most are determined in wind tunnels,
so your best bet is take some numbers from some known shapes and
approximate".
I am still searching for is a computer program (all my previous work was all
pre IBM-360 days) where I can put in the 3 dimensional body design, and let
the computer do all that daunting math, and tell me the Reynolds numbers and
air resistance. Then, of course, I'd like to be able to change the shape of
the body on the fly and see what effect various changes had, and see what
could be done to minimize the drag.
I feel sure that the guys at Lockheed and Boeing have wonderful systems
where they can fly their virtual airplanes around through lots of virtual
air and determine all sorts of things. (Hey! I can bring an autocad file!)
I also remember seeing or reading about some PC type systems that were used
by the America's Cup sailing guys to study hull shapes, but haven't been
able to relocate the information.
There are probably some general rules of thumb as well, don't put anything
flat on the front, or don't exceed a certain growth rate of length to
diameter, that I would be happy to know. Heck, for all I know there could
already be the perfect shape and it's down to who does the best job of
getting the mechanical stuff right.
Then again, I may be over thinking this whole thing. I continue to search,
will be very happy to learn from others experience of knowledge, and will be
happy to post back here anything interesting I find. Let me know if you
have any leads!
Thanks,
Jim.
P.S. As the day wears on and I got some research time.
I have found several 3D 'numerical wind tunnel' programs, some military and
not available outside DOD, and some from NASA - I have asked about
availability but have nothing back yet.
A very interesting paper at.
http://www.mech.soton.ac.uk/jrc/ME312/Auto_Aerodynamics_Notes.doc
Some excerpts:
"Simulation of the whole car flow (CFD, "numerical wind tunnel") will come.
It is currently possible on a rather simplified scale, but rapidly
developing. Still problems with size/speed of computers and with the
simulation of turbulence."
"Typical passenger car: Frontal area 1.8 to 2.1 m2
Weight 800 - 1800 kg
Typical drag coefficients 0.35 - 0.45. This has changed over time: see
diagram in lecture. Minimum at about 1950: main ideas of streamlining had
been sorted out, but regulations (higher lights), performance (wider tyres)
and styling (integral front wings, no running boards) worked in opposition."
"There is also non-aerodynamic drag (rolling resistance) which also
increases with speed, but nothing like so fast. Aerodynamic drag: 50% at 65
km/h, up to 80% total at 100 km/h."
"Drag reduction is very much in the region of diminishing returns and very
close attention to many very minor details. To quote one of the books I
looked up, if you want a CD of 0.5, just draw it and make it. For 0.4, do a
few confirmatory wind tunnel tests on a model. For 0.3, spend millions on
model and prototype testing."
-----Original Message-----
From: Elon Ormsby [mailto:ormsby1@llnl.gov]
Sent: Thursday, January 24, 2002 4:10 PM
To: land-speed@autox.team.net
Subject: Reynolds Numbers
James Waldron I think your answer is correct but by indicating drag is the
"cube" of speed might not precisely define the problem. Isn't drag the
square of the speed but power required is the cube of the speed? I think
the additional exponent is for acceleration and power is need for that as
well as overcoming drag. I mention this here because many times the
significance for the "cube" of the power is lost. Many think the power
required is only to overcome drag (a squaring function) and it ain't so. I
look forward to many more of your technically interesting contributions.
-Elon
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