It seems from my books that when flying the radius of a turn is equal to the TAS in knots, squared, divided by 11.26*tan (angle of bank)
So, lets say for Mach 2.2 the TAS is somewhere around 1200 kts, using a 30 degree turn...pretty extreme bank angle for an airliner...
Anyway, 1200^2 / 11.26*tan (30)
1440000/6.5
So, the radius of the turn would be 221505 ft or about 42 miles.
Meaning if you only turned 180 degrees you would end up over 80 miles adjacent to where the turn was started.
SlamClick From United States of America, joined Nov 2003, 10062 posts, RR: 71 Reply 5, posted (6 years 4 months 6 days 13 hours ago) and read 4748 times:
There is another way to figure it. Using this I get a very different result from the one above.
Standard rate turn is three degrees per second.
At three degrees per second how long to turn 180 degrees? Sixty seconds.
How far does one travel in sixty seconds at a given speed? That will half the circumference of the circle made by the turn.
Trick is, you can't work it from a Mach number without converting that to knots and you can't convert it to knots unless you know the temperature. The good news is it yields the answer in whatever units you choose. Input the speed in MPH, Knots or KmPH and the size of the circle will be in those units.
So, for this question he specifies Mach 2.2 and I'll assume ISA at Flight Level 600.
ISA temperature at FL600 is -56.35°C or 216.65° Kelvin. The speed of sound is 39 times the square root of the latter. So I get Mach one equals about 574 knots. Times our Mach number of 2.2 and I get 1263 knots True Airspeed.
1263 knots divided by 60 (minutes per hour) and I see that we are moving about 21 nautical miles per minute.
Well all the way around the full 360 would then be 42 miles.
The radius of a 42 nautical mile circle is only a bit over 13 nautical miles across.
Now because at one point we both got the figure 42 one might speculate that one of us was answering the wrong question. Problem is that 42 is the answer to life, the universe and everything, so it is pretty hard to sort out where one of us went wrong.
So I invite you to read through my explanation and see if I've made a mistake at some important point.
Happiness is not seeing another trite Ste. Maarten photo all week long.
David L From United Kingdom, joined May 1999, 9213 posts, RR: 42 Reply 7, posted (6 years 4 months 6 days 11 hours ago) and read 4690 times:
And while the answer is being considered, can I just throw a spanner in the works and point out that, in passenger service, Concorde's cruising speed was usually M2.00 to M2.02, not M2.20?
SlamClick From United States of America, joined Nov 2003, 10062 posts, RR: 71 Reply 9, posted (6 years 4 months 6 days 11 hours ago) and read 4661 times:
Quoting David L (Reply 7): Concorde's cruising speed was usually M2.00 to M2.02
I was wondering about that. Feel free to try my method with the new numbers if you feel strongly about it.
Happiness is not seeing another trite Ste. Maarten photo all week long.
Vikkyvik From United States of America, joined Jul 2003, 8200 posts, RR: 28 Reply 11, posted (6 years 4 months 6 days 11 hours ago) and read 4639 times:
AIRLINERS.NET CREW PHOTO SCREENER
Quoting SlamClick (Reply 5): Now because at one point we both got the figure 42 one might speculate that one of us was answering the wrong question. Problem is that 42 is the answer to life, the universe and everything, so it is pretty hard to sort out where one of us went wrong.
No matter, don't you see what you've done??? You've discovered the ultimate question!!! Well, almost...
Q: What is the radius (or circumference) of a 180-degree turn in an airliner at Mach 2.2?
A: 42
Now if only we can sort out that last bit about radius vs. circumference....
"Two and a Half Men" was filmed in front of a live ostrich.
Ralgha From United States of America, joined Nov 1999, 1614 posts, RR: 6 Reply 12, posted (6 years 4 months 6 days 11 hours ago) and read 4640 times:
Quoting SlamClick (Reply 5): So I invite you to read through my explanation and see if I've made a mistake at some important point.
Your explaination is correct for a standard rate turn, the problem is that at Mach 2, a 30 degree bank isn't anywhere close to a standard rate turn. One could figure out what the rate would be, but offhand I couldn't say.
I'll be back later with a formula if nobody beats me to it.
Dw747400 From United States of America, joined Aug 2001, 1244 posts, RR: 1 Reply 13, posted (6 years 4 months 6 days 10 hours ago) and read 4629 times:
Also, don't some large transport category aircraft use a four minute standard rate turn (1.5 deg/sec) in place of two minutes, primarily because of the airspeeds involved and to limit the needed bank angle?
FrancoBlanco From , joined Dec 1969, posts, RR: Reply 14, posted (6 years 4 months 6 days 10 hours ago) and read 4612 times:
Quoting SlamClick (Reply 5): 42 is the answer to life, the universe and everything
From flying the SSTSIM Concorde on MSFS (yeah, I know...), I have the original flightplans for the LHR-BAH (continuing to SIN) runs. In the late seventies they could not overfly Lebanon due to the civil war, so they did some spectacular looking turns in Syrian airspace to avoid the restricted area.
The technique was to use the aileron (elevon, actually) trim coupled with the Pitch Hold mode on the autopilot, in order to fly the aircraft with a constant five degree bank angle rather than strictly follow the special waypoints. At least, that's how I did it in the sim, it worked great.
The radius (circumference, anyone?) was rather impressive when cruising at M2.02 (that's the standard cruise speed, the autothrottle/autopilot always keeps the plane between M2.00 and M2.02 when in Max Climb/Max Cruise mode).
Sebastian
Edit: btw, 1263 KTAS would be a bit too high, I'd say. From what I know, the typical TAS would range between 1130 and 1160 knots. On www.groundspeedrecords.com the highest entry is 1205 kts GROUNDSPEED.
SlamClick From United States of America, joined Nov 2003, 10062 posts, RR: 71 Reply 15, posted (6 years 4 months 6 days 9 hours ago) and read 4574 times:
Quoting FrancoBlanco (Reply 14): btw, 1263 KTAS would be a bit too high, I'd say. From what I know, the typical TAS would range between 1130 and 1160 knots
Sounds about right. Remember that I was using M2.2 as in the thread title. The 574 knot SOS I got, times M2.02 gives me 1159.48 knots so - close enough?
Happiness is not seeing another trite Ste. Maarten photo all week long.
SlamClick From United States of America, joined Nov 2003, 10062 posts, RR: 71 Reply 18, posted (6 years 4 months 6 days 8 hours ago) and read 4537 times:
Rule of thumb: Put your thumb over the instrument concerned, at arm's length. If you thumb covers the difference your answer is close enough.
As Nathaniel Bowditch used to say: "One should take care not to solve navigation problems to too many decimal places. It produces an illusion of accuracy." Well if he didn't say something like that he should have.
Happiness is not seeing another trite Ste. Maarten photo all week long.
FrancoBlanco From , joined Dec 1969, posts, RR: Reply 19, posted (6 years 4 months 6 days 8 hours ago) and read 4530 times:
...and since we both know that the average population of the universe is zero and therefore the population of earth must be zero, this discussion is of no use for anyone. Not even for the 42 mice strolling around on my desk.
Nevertheless, that's a great quote you cited, nevermind if he said that or not.
Futurecaptain From , joined Dec 1969, posts, RR: Reply 20, posted (6 years 4 months 6 days 8 hours ago) and read 4513 times:
Quoting AirSpare (Reply 10): Mach 2.0, that was without the optional Improbabilty Engines?
And were the flux capacitors operating or no?
Quoting Ralgha (Reply 12): Your explaination is correct for a standard rate turn, the problem is that at Mach 2, a 30 degree bank isn't anywhere close to a standard rate turn. One could figure out what the rate would be, but offhand I couldn't say.
See if this formula I have makes sense.
(Rate of turn in degrees per sec) = 1091*tan(bank angle) / Velocity (knots)
So, we want 3 deg/sec for standard rate at 1160 kts.
A342 From Germany, joined Jul 2005, 4655 posts, RR: 4 Reply 21, posted (6 years 4 months 6 days 8 hours ago) and read 4480 times:
I have read the following about the SR-71: At cruise speed and a bank angle of 35 deg, the distance flown on a full 360 deg circle is 320 km. That would give a turn radius of 51 km. Unfortunately, the exact speed was not stated, but it must be something around M3.0, no ?
Maybe you can work out something with your formulas...
SlamClick From United States of America, joined Nov 2003, 10062 posts, RR: 71 Reply 22, posted (6 years 4 months 6 days 8 hours ago) and read 4474 times:
Quoting A342 (Reply 21): the exact speed was not stated, but it must be something around M3.0, no ?
The SR-71 operators usually don't admit to much over Mach 2.0 so the numbers might be more in that range. That being the case we are talking about a radius of 28 nautical miles which is as good as anything I've read or posted so far.
Happiness is not seeing another trite Ste. Maarten photo all week long.
Prebennorholm From Denmark, joined Mar 2000, 6016 posts, RR: 55 Reply 23, posted (6 years 4 months 6 days 5 hours ago) and read 4396 times:
Quoting SlamClick (Reply 5): There is another way to figure it. Using this I get a very different result from the one above.
Standard rate turn is three degrees per second.
Huh, you just don't turn three degrees per second going at Mach 2. Certainly not with pax on board.
Quoting SlamClick (Reply 18): As Nathaniel Bowditch used to say: "One should take care not to solve navigation problems to too many decimal places. It produces an illusion of accuracy." Well if he didn't say something like that he should have.
Charley Brown, talking to himself: If I make one mistake each day, and I if I die at age 80, then I will have made approximately 30,000 mistakes.
When calculating my mistakes it is best to stick to round figures.
Quoting Oly720man (Reply 2): Not sure if concorde ever pulled a 30 deg turn at cruise, but the distance of around 40 miles looks to be the right ballpark.
And if you were doing it at M15 you'd be half way across America...
Dear Oly720man, your Mach 15 turn half way across America is a 2G turn. A level 2G turn requires a 60 degrees bank. At 30 degrees bank you could add Canada and Mexico to your flight profile.
New subject: The flight profile of a low orbit satellite can be compared to a plane making a 2G horizontal turn. One G to keep altitude and one G to produce the turn.
A satellite constantly makes a one G vertical turn - it falls down against terra firma, but misses since Columbus uninvented the flat Earth. It makes a 360 degrees turn in 90 minutes = 5400 seconds. It's standard turn rate is 360 divided by 5400 = 0.06666 degrees per second. (Let's call that 0.07 degrees to please Nat Bowditch).
But who knows what is right and wrong? The other day a colleague from Sydney, Australia told me that in the sea east of New Zealand the water falls over the edge.
Always keep your number of landings equal to your number of take-offs, Preben Norholm
SlamClick From United States of America, joined Nov 2003, 10062 posts, RR: 71 Reply 24, posted (6 years 4 months 6 days 5 hours ago) and read 4382 times:
Quoting Prebennorholm (Reply 23): Huh, you just don't turn three degrees per second going at Mach 2. Certainly not with pax on board.
Sorry, I haven't logged much time at Mach 2 (meaning none) and hadn't thought that one all the way through. Someone else posted that three degrees per second at that speed would be a 72.6 degree bank. Bit steep!
I believe I am well ahead of schedule and could die any time now.
Happiness is not seeing another trite Ste. Maarten photo all week long.
25 2H4: A perfectly normal Southwest Airlines procedure for turns to final. Just ask the Civil Aviation forum..... 2H4
26 Chksix: With the help of this manual: http://www.sr-71.org/blackbird/manual/ you can make accurate calculations for the Blackbird. Cruise speed was 3.2, bank
27 Prebennorholm: Please don't do that! A.nut would suffer badly.
28 2H4: Indeed. Remember, SlamClick, you've still got a book to write..... 2H4
29 EGTESkyGod: The way to find out is to ask someone who has done it. GDB was onboard Concorde for an evaluation flight on September 11th 2001 where Concorde was flo
30 Kaddyuk: I knew there was a reason you were on my RR list... Thanks for the funniest post this week!
31 David L: No, that's OK. One idea a month (good or bad) is quite enough for me, thanks.
32 Kaddyuk: You joke around but I swear my pilot on WN the last time i flew SJC-LAX was straight out of the Navy and Honestly believed he was performing a Nimitz
33 Bellerophon: A380900 ...I was wondering how much pilots were able to turn when the concorde was at full speed... Concorde manoeuvred very well at high speed, she j
34 David L: Well, that's that settled! Thanks, Bellerophon.
35 MidEx216: You guys are nuts. I've finally found my family!
36 Helvknight: {ROTFL} I've been meaning to do this for a while. Slamclick, you have just joined Zeke and Wings on my RU list.[Edited 2007-01-23 23:00:44]
37 A380900: Bellerophon, Thank you. I was waiting for a concorde pilot to settle the matter! I thought that it was like a super tanker in the sky. Barely able to
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