Not always. But that would mean a rate of constant turn, Don't you think that a pilot would discover the fact that he's been pressing the left or right rudder with the same pressure every time the air was calm?
Here's a tidbit I tossed off a while back:
Assume:
800 MPH aircraft = 357 m/s
radius equator: 6445 mi = 10.37 E6 m
Calculating the acceleration felt from turning in the circle assumed above:
angular acceleration = v^2 / r = 357^2/10.37E6 = 0.0123 m/s^2
That's not very much acceleration. Now calculate the degree of roll needed to keep the airplane at altitude while making this circle:
Assume:
acceleration due to gravity = 9.8 m/s
acceleration due to turn = 0.0123 m/s
Degree roll = arctan(0.0123/9.8 ) = 0.072
That is a very small amount of roll, even at such high speeds. You would NOT notice such a small turn. A pilot would follow his instruments which probably have an accuracy on the order of 0.5 degrees or higher, correct me if I'm wrong.
Ah, no.
You've confused angular acceleration with acceleration at an angle.
Here are the results of my analysis:
Distance at Equator: 6,378,000m
Speed 510 MPH (I though this might be a more acceptable speed.)
230 m/s
| Latitude | Distance (m) | Time (s) | Acceleration (m/s^2) |
| 79 N | 190,000 | 830 | 0.39 |
| 45 N | 800,000 | 3,500 | 0.093 |
| 0.0 | 1,600,000 | 7,000 | 0.046 |
| 45 S | 2,400,000 | 10,000 | 0.033 |
| 79 N | 3,000,000 | 13,000 | 0.025 |
I chose to stay at two significant digits.
I decided to send the plane on a due east (or west) heading and have it travel one-fourth of the
way around the FE.
The distance calculation assumes that latitudes are equidistant, and therefore proportional to each other.
The time calculation is based on v=d/t. The acceleration is based on vector addition of the velocity changes, one back + one north = square root of 2 at 45 degrees, divided by the time.
The differences in flight times would be difficult to explain, varying by more than 10 times in one case.
The accelerations are significant enough to cause rolling of round objects such as pens since many coefficients of rolling friction are less than the accelerations in the table above. I don't have engineering estimates, but I also believe that glossy magazines laid open on the
seat tray would slide, for example.
I hope that helps. It is a challenging problem.
Gulliver