From: larry@ichips.intel.com
Newsgroups: sci.military
Subject: Re: SR-71 top speed estimates
Date: 15 Apr 92 04:27:09 GMT
Organization: AT&T


From larry@ichips.intel.com



Kenneth D Rolt writes:
>>what is the true top speed of the aircraft?

Phil Moyer responds:
>The "SR-71 Supersonic/Hypersonic Research Facility Researchers Handbook",
>published by NASA, 

Actually Phil, that handbook was published by Lockheed. That's where I got it
from. It was distributed to NASA, among other places. I think it is important
to try and use the data in the handbook, since the intention of this series
of volumes (of which this one is the first) is to give a technical presentation
on the SR-71. The first volume was an executive summary.

>                   has (on page 11) a Dynamic Pressure Range listed.  Using
>that set of numbers (325-847 lbs/sq.ft), it is possible to back-calculate
>a theoretical equivalent velocity.  At 85,000 feet, that velocity is
>3,410 mph.  Using the speed of sound at 85,000 feet (663.6 mph), that equates
>to Mach 5.14.  No, that's not a typo, that's Mach five-point-one-four.
>
>[Thanks to Larry Smith for these calculations.  -prm]

You're welcome Phil, however I WAS very surprised at my results. I have been
one of these people who believe that the top speed of the SR-71 is under 
Mach 4. But, a result is a result so I posted it hoping to get criticism.
Guess I succeeded. You learn though by making mistakes!

Let me reproduce a copy of that page so that people can see
what prompted the calculation:


                    Lockheed SR-71
       Supersonic / Hypersonic Research Facility
                 Researcher's Handbook
               Volume I  Executive Summary (Continued)

Pg. 11

Flight Envelope

      - Maximum Performance
             Mach 3.2+

             Altitude: Above 85,000 Feet

      - Airspeeds
             310 - 450 KEAS (Normal)

             500 KEAS (Extended)

      - Dynamic Pressure Range: 325 - 847 lbs/ft

      - Heat Soak: Over 600 F for 60 minutes

      - Remain at Mach 3.00: Over 60 Minutes Per Sortie

Now another key piece of information here is that Ben Rich (the former head
of Lockheed ADP (Skunk Works) has told me personally, that even though the
airplanes are now being heavily declassified because they are going to
museums etc., there are a few things that are remaining classified. One of
them is the top airspeed and altitude of the aircraft. 

Also, there have been former SR-71 pilots that have spoken in the past year 
or so of speeds in the Mach 3.7-Mach 3.8 range as well.
Also there were proposals by P&W to enhance the J-58. There was even a
rumored engine mod made available for testing. Anyway treat all this as
rumor. The importance of it is  that it provides motivation to attempt to
calculate a top speed if it seemed possible to do so. One knows that the
preferred operational altitude of this airplane is in the >75,000 ft range.
The reproduced page above mentioned > 85,000 ft. The recently published
OXCART History mentions that A-12's were capable of > 90,000 ft. So I decided,
"what the heck", take 85,000 ft and calulate a airspeed for the mentioned
dynamic pressure. That calculation is reproduced below in its entirety.
I copied the entire posting.

--------

Sorry guys, I HAD to try this, since we don't have the equation
for the supersonic KEAS to Mach No. formula!! If I skrewed up,
I'm sure someone will spot it and we'll at least know a little
more.

Pg. 11 of SR-71 Researcher's Guide mentions a Dynamic Pressure
Range of 325 - 847 lbs/ft (should be 325 - 847 lb/sq.ft)

I thought I would try to calculate an equivalent Mach No. for said
maximum dynamic pressure at 85,000 ft. using a Standard Atmosphere Chart
in Eng. Eng. Units., from "Introduction To Flight" by J.D. Anderson,
3rd. ed.


Step I) Calculate Velocity at 85,000 feet

The equation for all kinds of dynamic pressure
compressible/supersonic/hypersonic is:

DynamicPressure = 1/2 (density) (Velocity ** 2)

At 85,000 feet, density is 6.7706 E-05 slugs/cu.ft.
  via a Standard Atmosphere Chart in English Eng. Units

So:

847 lbs/sq.ft = (1/2) X (.000067706 slugs/cu.ft.) X (Velocity ** 2)

1 lb force = (1 slug) X (1 ft/sec**2) (equation does balance in units)

847 = .000033853 X (V**2)

25,019,939.15 fps = V**2

5002 fps = V

5002 fps X (60 mph/88 fps) = 3410 mph



II) Calculate Speed of Sound at 85,000 ft.

speed of sound = ( (lambda) X (R) X (T) ) ** 1/2

R = Specific Gas Constant
	1716 ft lb/(slug)(degrees Rankine)
T = Temperature from Standard Atmosphere Chart in Deg. Rankine
        for 85,000 ft. = 394.32 deg.R
lambda = ratio of specific heats (a constant here eq. to 1.4)

So:

speed of sound at 85,000 ft in (fps) = (1.4 X 1716 X 394.32) ** 1/2
		= 973.3 fps X (60 mph/88 fps) = 663.6 mph



III) Calculate Mach No. at 85,000 ft.

So:

 Mach No. = Velocity at 85,000 ft / Speed of Sound at 85,000 ft.

M = 3410 / 663.6 = 5.14 !!

Mach 5.14 at dynamic pressure of 847 lbs/sq.ft at 85,000 ft (??) (!!)

I must have skrewed up somewhere!

Larry

-----------

smpod@venus.lerc.nasa.gov (Stefan) responds:
>I think that there is something wrong with your calcs: Mach 5 is the beginning
>of the hypersonic range and I highly doubt that the SR-71 is that fast without
>aero-heat problems. Using 
>
>          dynamic pressure =density*velocity**2/2 or 
>          dynamic pressure =pressure*gamma*Mach Number**2/2
>
>Using 847 lbs/ft**2, I get M=2.34 approx.
>
>It seems that NASA is using the Sr-71s in a convervative regime.

Thanks Stefan for the help. I rederived your second equation for dynamic
pressure and it is correct. So I used it with the following arguments in
EE units:

dynamic pressure =pressure*gamma*Mach Number**2/2

Given:
  Ambient pressure at 85,000 ft = 45.83 lb/ft**2 (from above source)
  gamma = 1.4
  dynamic pressure = 847 lb/ft**2
Find:
  Mach Number

So:

847 = 45.83 X 1.4 X MachNo**2 / 2
847 = 32.081 X MachNo**2
26.402 = MachNo**2
5.14 = MachNo   (it agrees with the other formula for dynamic pressure that
                 I used above)

The interesting thing is to try the calculation on the lower range of dynamic
pressure of 325 lb/ft**2 given in the Lockheed Handbook, also at 85,000 ft.

dynamic pressure =pressure*gamma*Mach Number**2/2

Given:
  Ambient pressure at 85,000 ft = 45.83 lb/ft**2 (from above source)
  gamma = 1.4
  dynamic pressure = 325 lb/ft**2 (the lower range given in the Lockheed book)
Find:
  Mach Number

So:

325 = 45.83 X 1.4 X MachNo**2 / 2
325 = 32.081 X MachNo**2
10.130607 = MachNo**2
3.18 = MachNo   (this also agrees with the other formula for dynamic pressure
                 when 325 lb/ft**2 is used)

The interesting thing here is that this is close to the Mach 3.2 "official"
top speed for this bird.

Mary Shafer responds:
>That can't be right.  The maximum Mach at 85,000 ft is 3.3 and we routinely
>fly at 3.2 (I've just trotted down the hall and checked with one of the
>backseatters.  She and I looked in the Dash 1.)

Thanks Mary for your time expended on this. I knew we'd get to the bottom
of this if we could get a real flight test engineer to look at it.

>The limits are not as simple as you've set forth.  If you look at the
>flight envelope you'll see that there are a number of limits at
>different places.  For example 847 psi may be the limit at lower
>altitudes and Mach 3.3 may be the limit at higher altitudes.  You
>cannot assume that the highest q-bar is at the corner of the
>envelope--it almost invariably isn't.

Well, this IS VERY helpful!! See I learned something! I learn by screwing
up sometimes. There was no associated altitude for these dynamic pressures.
I will try and find out from the guy who sent me the Lockheed Handbook.

>In this case the Mach number sets the limit because of the impingement
>of the shock on the vehicle. 

You're talking about the inlet cowl lip here I assume because at on-design
speed the spike cone shock is on the inlet lip. Ben Rich confirmed this as
well. Actually not all impingements are bad. There are just certain types
of impingements that get REAL nasty at higher mach Nos. Basically they
form a plasma torch and cut through enything (from the hypersonics class
I took).

>(Q-bar is usually in psi, not psf--are you sure about this?)

As you can see from the repro of the Lockheed Handbook above.

>Phil> [Thanks to Larry Smith for these calculations.  -prm]
>
>I'm not sure you should thank him--he's led you badly astray.

Wrong!

I made an honest attempt at calculating something. The data was there and
I was curious. I'd do it again. As a matter of fact I intend to do more
calculations of this sort with this airplane as the subject. Unfortunately,
I'm not at all affraid of being wrong. I don't try to be wrong though.
As I said it was a learning experience.

In my original posting on skunk.works I questioned my results. Quoting 
myself at the end of my original posting on this subject (see above as
well):

"Mach 5.14 at dynamic pressure of 847 lbs/sq.ft at 85,000 ft (??) (!!)
I must have skrewed up somewhere!"

I clearly offered my calculations to the skunk.works group for criticism. I
wish you would have criticized them then. However thanks for your criticism
of the calculations, and your valuable input.

Regards,

Larry