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What is the minimum turning radius of an SR-71 at Mach 3.2 and an altitude of 80,000 feet?

I have heard that if an SR-71 were to cross the Pacific coast over San Francisco and pull a hard turn to the right, it would return over Seattle.

I'm interested in real-world performance, taking into account things like inlet unstart (failure to capture the engine inlet shockwave in the intake) from too sharp an angle of attack.

Rodrigo de Azevedo
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Mark
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4 Answers4

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The Turn Radius of the SR-71 would depend on its speed. The faster it went the wider its turn radius was.

The SR-71 had a minimum turning radius at altitude of about 80 nautical miles (NM) . It was not an airframe limitation but a matter of wing area. At 80,000ft, the air is too thin and the wings too small to allow for much lift to turn with.

At a turn radius of 80 NM, the SR-71 would cover about 145 miles, taking about 4 minutes in the process of making a 180 degree turn.

Details are provided in the SR-71 flight manual handbook, which is now declassified: Fig. 1-9, SR-71 handbook

voretaq7
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DSarkar
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  • What is the turning radius at mach 3.2? –  Aug 06 '14 at 19:20
  • Check Figure 1-9 http://books.google.co.in/books?id=voPlAwAAQBAJ&pg=SA1-PA11&lpg=SA1-PA11&dq=turning+radius+at+mach+3.2&source=bl&ots=dr5oLR4Tho&sig=TGRKTrot7X8ucsCxnRuJ_8xK5t4&hl=en&sa=X&ei=nZDiU6fBHMOKuASEzYDoBQ&ved=0CFAQ6AEwBw#v=onepage&q=turn&f=false – DSarkar Aug 06 '14 at 20:39
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    @D_S Why? Is that where the answer is? If so, it should be in your answer here, too. –  Aug 06 '14 at 22:41
  • Yes , that's where the answer is . And No , it cannot be in my answer because I do not have permission to re-produce the figure. – DSarkar Aug 07 '14 at 08:02
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    i looked at the figure. It does not list the minimum turning radius at 80,000 feet at mach 3.2. Including your interpretation of the relevant portion of the figure here is not a violation of copyright. –  Aug 07 '14 at 08:06
  • @D_S I can't imagine Lockheed Martin would object to reproducing this under the Fair Use doctrine: this would qualify as an "educational purpose", only a small portion of the overall work is being reproduced, and as the document is a (declassified) government work freely available to the public there is no impact on the market for / value of the work. If they take exception to the image being included here I'll gladly take the hit :) – voretaq7 Aug 07 '14 at 17:50
  • @voretaq7 Thanks. Still, that chart doesn't indicate that 44° is the maximum angle of bank (what if you could turn tighter by banking at 48°, for example), and it doesn't say that it is for a density altitude of 80,000 feet. Also, even taking the chart at face value, it gives a radius of ~51 NM for a 44° bank turn at 3.2 mach, which doesn't correspond to D_S's answer of 80 NM turn radius. –  Aug 07 '14 at 17:55
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Please use the equations of this answer. The numbers might be different, but the physics are the same.

EDIT: Thanks to D_S for providing the link to the manual.

When flown with the maximum allowable load factor of 1.5 g at 80.000 ft (48° bank), the turn radius at Mach 3.2 (equivalent to v = 953.3 m/s in 80.000 ft) will be 83.5 km. To be more precise, you will need to add the effects of earth rotation, but for now I leave this away. As you can see, the turn will still need 163 km or 103.7 miles, but not the distance from San Francisco to Seattle which is more than 6 times bigger.

To turn this around: A circle at Mach 3.2 which has a diameter of 1092 km requires a bank angle of 9.6°. That can hardly be called a turn.

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Peter Kämpf
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    The equations are nice from a theoretical standpoint, but you need to pick your assumptions when using them. The SR-71 is so far outside of "normal" for airplanes that I don't know what assumptions are reasonable. – Mark Aug 06 '14 at 09:31
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    @Mark: I refined my assumptions, but the SR-71 was not so unusual that it would violate the laws of motion. Those equations are valid for all airplanes. – Peter Kämpf Aug 06 '14 at 09:44
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    The equations are valid. But the maximum possible load factor is an argument we need to know. The load factor not only needs to be allowed, but also achievable at cruise altitude and speed. – Jan Hudec Aug 06 '14 at 12:37
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    @Jan Hudec: At Mach 3.2 the possible lift is out of the question - increase angle of attack, and the lift will be there. The main problem is the drag increase which could be more than the engines can compensate (and the efficiency of the intake at the different angle of attack). 1.5 g should not be an issue, however, if the airplane was flying level with some margin before. All it needs is half empty fuel tanks, and there is plenty of margin already. – Peter Kämpf Aug 06 '14 at 13:58
  • Why is your answer different than D_S's? –  Aug 07 '14 at 13:18
  • @Articuno: Because I use the formulas, and he some general figure. Besides, we are not so far apart. 80 NM are 92 miles, not so far off the 103.7 I have as a result. His result is valid for Mach 3.0 (the book page mentioned in the comments), my result is for Mach 3.2, as asked by Mark. Turning any tighter than that circle with 103.7 miles diameter at Mach 3.2 would violate the aircraft limits, though. – Peter Kämpf Aug 07 '14 at 13:43
  • So, her/his answer is what is physically possible, and your answer is what is legally possible? –  Aug 07 '14 at 16:00
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    @Articuno: More than that. The diameter grows with the square of the speed (please look up the formulas in the first link in my answer!). His 80 NM at Mach 3.0 translate to 91 NM at Mach 3.2 or 104.7 miles. This leaves just a rounding error between both results. My answer is both physically and legally correct, and actually answers Mark's question. – Peter Kämpf Aug 07 '14 at 16:19
  • Thanks. If D_S's answer is based on Mach 3.0 rather than Mach 3.2, that's not even answering the question. Although, I can't even tell where D_S's answer commits to a particular speed. –  Aug 07 '14 at 16:21
  • @Articuno: In a comment D_S linked to Figure 1-9 in a book. If you look up the link, it gives you the conditions for his number. Yes, that is StackExchange: Not always goes the highest score to the correct answer. We are all humans, after all. – Peter Kämpf Aug 07 '14 at 16:24
  • I looked at that chart, but it doesn't give conditions for his number. It gives values over a large domain, and doesn't even say that the entire domain is physically achievable at 80,000 feet. –  Aug 07 '14 at 16:25
  • @Articuno look at the temperature mentioned above the chart and then check the definition of standard atmosphere: you'll find that is the temperature you have above 36000ft till 66000. 80000 is slightly "warmer" but not much. – Federico Aug 07 '14 at 17:12
  • @Federico That is my point. It doesn't commit to a particular density altitude. –  Aug 07 '14 at 17:24
  • @Articuno: Density is not so important. What counts is true air speed, and with the temperature we can convert Mach to TAS. I also used the Standard Atmosphere (from 1963) for my result, so both the chart and my result yield the same radii. The chart stops at 44° bank with a radius of 51 NM; if you use the equations in my link, at 44° the radius will be 15% bigger than in my result. Close enough! – Peter Kämpf Aug 07 '14 at 18:29
  • @PeterKämpf Is the maximum level-flight, 1.5G angle of bank 44° or 48°? –  Aug 07 '14 at 19:06
  • @Articuno: The bank angle is the arccos of the inverse of the load factor. For 1.5g, the inverse is 0.6667, and the arccos of that is 48.1597 degree. If the pilots fly the turn without sideslip, this is the bank angle that produces a load factor of 1.5, which is the limit for the SR-71 above Mach 2.6 (see page 5-8 of the manual). – Peter Kämpf Aug 07 '14 at 19:40
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Considering the current flight status of the SR-71 (retired) it's maximum speed will depend on the tug moving it and the turn radius is probably around 30-40 meters depending on how far the nosewheel pivots.

paul
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I worked one in about 1989 that was flying eastbound toward Rapid City, and started his turn back toward Edwards. He rolled out over GLL VORTAC, so about 200 nautical miles south of where he started. He was at roughly 2400 knots (He slowed down for the turn). Altitude was above FL600, but we did not get information on actual altitudes.

atc_ceedee
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