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I see a couple things wrong with the math. First, 2435.86 mph at Mach 3.2 implies Mach 1 = 761 mph. That's true at sea level. In reality, the SR-71 does its thing at, what, 80,000 feet? Plug that altitude into a standard atmosphere calculator (there are many on the web) and get 667 mph. So Mach 3.2 at 80,000 feet equals 2130 mph, not far from the 2193.2 mph "party line" speed quoted earlier.
The second problem is excessive precision in that calculated value of 2435.86 mph, which has six significant digits of precision. On the other hand, the illustration is marked "Mach 3.2." That has two significant digits. You've heard the saying, "garbage in, garbage out." Well, there's no magic way to get output accurate to six digits from input accurate to two digits.
The rounding error in 3.2 could be a few hundredths, and each .01 Mach at 80,000 feet is about 7 mph, so really it makes sense to round mph to the nearest multiple of 10 or the nearest whole number. Of course you can calculate to .01 mph, but the decimal part is just garbage.
Yea, but your math teacher more than likely didn't design an aircraft that flew more than mach 3 or for that matter any aircraft that established a speed record that was recorded by the FAI - some in "six significant digits of precision."I knew a math teacher who had his students compute the diameter of a tree trunk with a tape measure of its circumference. Left to their own devices, most gave the answer to 10 digits because that's what their calculators said. A few with superior instinct for numbers would give the result to the nearest inch. They understood the unavoidable errors in the process made higher precision unrealistic. Garbage in, garbage out.
The "Party Line" is what the aircraft was actually clocked at in 1976, and what was accepted as a world's speed record by the Fédération Aéronautique Internationale (FAI), it's their math, not mine.
Again I think you're trying to split hairs - that illustration is from a USAF technical publication probably developed with the assistance of the manufacturer. It was printed to show maintainers how the system worked at projected speeds. So tell you what, for argument's sake let's just round out your calculations to the lowest mach number. BTW, if you think this is sooo wrong there are dozens of world speed records presented this way. Here's a few:
Yes, exactly. That number is within 3% of my conversion from Mach 3.2 to mph, which suggests I didn't go far wrong in my math.
I don't see what that has to do with the discussion since nobody ratifies a speed record based on a book figure. The plane has to be timed over a known distance. For example,
1990 SR-71 record flight
See chart #3. The speed course is a set of "timing gates" defined by latitude and longitude. Distance between gates is calculated to 0.01 mile and the times were taken to 0.01 second. From that they calculate speed to 0.01 mph. That's reasonable because the inputs to the computation are so precise. It's not reasonable to believe anything like that can be achieved from a single number in a maintenance manual.
But really, I don't see it as a big deal if a number has an excessive number of decimal places — as long it was computed correctly. That's where I think you went wrong getting 2435.86 mph from Mach 3.2. Dividing one by the other gives 761.206 mph = Mach 1. That number is easily verified online, for example,
speed of sound
But there's a catch. That speed is valid at standard sea level conditions, and no SR-71 hit Mach 3.2 at sea level. What we need is the speed of sound at some nominal cruise altitude, say 80,000 feet. No problem. There are many online calculators for standard atmosphere properties. For example:
1976 standard atmosphere calculator
Enter 80,000 feet geopotential altitude (that's how aircraft altitude is normally expressed) and read 977.822 feet per second as the speed of sound. That equals 666.697 mph, not 761.206.
In that calculation I indulged in excessive decimal places myself. Remember that I picked 80,000 feet. The book illustration doesn't give an altitude, so I just guessed 80,000 would be a reasonable value. But what if the SR-71 is flying at 81,000? Then I get 978.496 fps = 667.156 mph. That's almost half a mile per hour faster. Thus, my three decimal places are excessive since altitude is such a wobbly number.
But let's run with the speed of sound at 81,000. Then Mach 3.2 = 3.2 times 667.156 mph = 2135 mph. That's 200 mph different from your 2435.86! If you still stand by that speed, show how it's calculated. Present a convincing argument, and I'll own up to being wrong!
I knew someone who flew in one and said that they hit Mach 3.4 on the flight. He was in the rear seat and just being transported (not a flight crew). The pilot hinted that the plane could go faster.
Do you want a lollypop or plastic trophy?!?!
The point behind this post is for many years the SR-71's top speed (mach, MPH, knots, kps, whatever) was never found in a technical publication made available to the public!!!!!
AND - the aircraft was able to fly faster than what was indicated in the 1976 speed record!!!!
Now put it to bed and stop acting like Sheldon Cooper!!!
I don't want any trophy, just a civilized discussion. It's not necessary to shout. I would have expected a moderator, of all people, to be a model in that respect. If you goofed the math, OK, it happens. And with a large and technically astute readership, someone will notice your slip. Years ago, in an astronomy discussion group, I posted my own precise calculation of the time when the approaching equinox would occur. It didn't take long before somebody explained that the formal definition of "equinox" was based an a different angle than my computation. In other words, my "right to the second" value was in reality only accurate to a minute or so. Oops.
When that happens, just tell yourself public embarrassment is a small price to pay for getting smarter. Nowadays when the subject comes up I can give precise equinox and solstice times, and they really are accurate to the second, thanks to that guy who corrected my mistake. I can't remember the name, but whoever you were, thanks. You made me a stronger man.
Getting back to the SR-71, the pilot manual was declassified years ago and can be bought in printed form. It's even online. Here's a graph of its limit speed. (The engine airflow illustration in your first post is also in the manual.)
limit speed and altitude envelope
Towards the end of its career it appeared in airshows in Europe. I remember reading about its flight to UK, it started slowing down above the Atlantic in the region that used to be called "The Western Approaches" by the Royal Navy.I talked with a former SR-71 pilot who said there were two top speeds: Maximum controllable speed and maximum speed.
At the max controllable speed, it more or less went where it was supposed to go. At max speed, you could be over a different state from where you intended, but you were definitely going fast.
His statement was, "You've never been lost until you're lost at Mach 3!"
His second statement was, "if you're going Mach 3, it had better be pointed toward the fuel ..."