The new forums will be named Coin Return (based on the most recent vote)! You can check on the status and timeline of the transition to the new forums here.
The Guiding Principles and New Rules document is now in effect.
Physics/math question
Organichu
poopspeesRegistered User regular
poopspeesRegistered User regular
Something I was thinking about earlier... also assume that the angle of rise of both planes is equal, and that they begin their loops at their given speeds and their speeds do not change.
See, I'm thinking the answer is almost surely yes... but then I wonder, does the extra displacement (should be twice as much, right?) 'negate' because of the 'twice as much' speed? If it was linear (say, make four left turns with right angles) I wouldn't ask the question, but I'm just trying to ensure that there's nothing that I'm forgetting from 10th grade Geometry about the properties of circles.
See, I'm thinking the answer is almost surely yes... but then I wonder, does the extra displacement (should be twice as much, right?) 'negate' because of the 'twice as much' speed? If it was linear (say, make four left turns with right angles) I wouldn't ask the question, but I'm just trying to ensure that there's nothing that I'm forgetting from 10th grade Geometry about the properties of circles.
Organichu on
0
Posts
I'm equating "angle of rise" to two cars going at two different speeds, but with the steering wheel turned the same amount in each car, if you know what I mean.
Possibly, spatial awareness is something at which I'm terrible.
Like, ok. If I am at an 80 degree angle upward, it doesn't matter whether my speed is amazingly high (200,000 mph) or amazingly slow (2 mph)?
I guess it makes sense, but my visceral reaction is that since I'm moving faster, I'm moving more and more distant from my flight plan... though I guess I can't articulate it.
Right, if both planes are turning at the same "angle", they'll go the same distance, the second in half the time.
The reason it feels weird is that it's not a realistic example. Planes can only turn so sharply, and I imagine it's limited in a large way by how fast they're going. In general, a slow plane will be able to maneuver a lot better than a fast plane. It wasn't specified in the question how sharp they turn, though, which is necessary to answer it.
IOS Game Center ID: Isotope-X
I'm not sure this is even a vertical loop. The root of the problem doesn't care about these things, so make it so they're circling a runway or something on the horizontal plane to prevent all this crap from interfering.
Anyway, the geometry part of the problem seems that they would have to travel the same path. If they do travel the same path then the plane going twice as fast would get there in half the time. If they don't travel the same path I don't see an easy way to calculate how far the second plane would travel...couldn't it travel infinitely many radii?
Edit: This may help you out. Circumference of a circle is C=2*pi*r, or C=pi*d.
To illustrate this, imagine a car going around a (steeply banked) 30-yard-diameter track at 1 mile per hour, then the same car going around the track at 5, then 20, then 60 miles per hour. The car travels the exact same path (same distance) for each, but the car going 60 mph will reach its starting point 60x faster than the car going 1 mph.
I think your "visceral feeling" is usually correct, because in regular conditions (say, a large parking lot), the above would never work: as you increase your speed the car's angular velocity will overcome the car's traction, causing the car to slip, increasing the total distance traveled. This traction problem doesn't really come into play here, though.
Also, I'm pretty sure that if you double a plane's speed, you quadruple the angular velocity, so the pilot would feel 4x the Gs during the second loop.
Edit: wherever I say "angular velocity" above, I meant "angular acceleration".
Let's say the angle of ascent into the loop is 30 degrees, ok?
one is going 500mph, or approximately 140 m/s.
The other, 1000mph or approximately 280 m/s, yes?
So the X component, (how far the airplane would travel on the X direction) would be
140m/s*cos(30) = 121 m for the 500mph aircraft and
280m/s*cos(30) = 242 m for the 1000mph aircraft.
So the faster aircraft travels twice as far in a given length of time, in both the X and Y directions. Seems to me that they'd both complete 1 loop in the same time, but the second aircraft's loop would be larger, be it 2 (I think) or 4 times larger.
Anybody? Bueller?
I agree that the faster aircraft travels twice as far in a given length of time. Since they have the same angle of ascent, though, both aircrafts are going to travel the same loop, and therefore the faster aircraft will do it in half the time.
That...I don't think you're making sense. If you have 2 vectors, and one is 121m @ 500mph and the other is 242 m @ 1000mph, the second is clearly bigger, yes?
What you're saying would be try, if the airplane were attached somehow to a central point. Is that what you're assuming? That's the only way I can see what you're saying being correct.
What I think you meant by it was that your "angle of rise" is the change in your pitch in a given amount of time, most likely per second. So if you started out flat and had an AoR of 60 degrees, it would take you 360/60 = 6 seconds to level out again after completing a loop whether you were going 0 miles an hour or a million. If that's right, then both loops would take the same amount of time to complete, with the faster plane in your example going in a loop with twice the radius/diameter/circumference.
I thought of it on my own, it's not an assignment.
Iceman.USAF's thinking makes most sense to me, but as I said, I'm pretty confused by it lol.
In reality though, I think the faster plane would follow a larger path. Planes act more like boats on water than cars on a road, and a turning boat will "drift" or "skid" across the top of the water in a corner.
This is what I'm looking at, yes.
I guess I can save everyone a lot of trouble.
I'm driving a Porsche. I put it to 50 MPH and turn left as hard as I can until I'm back at my original point.
I wait 10 seconds.
I'm driving a Porsche. I put it to 100 MPH and turn left as hard as I can until I'm back at my original point.
Same size 'traction circle'?
If they go the same amount of time before turning, this would be the result. That means they go 1 second or whatever and then bank the same degree. If they are constantly turning, I think it should still work like this (the same amount of time being constantly banking). I'm trying to make this a vector problem.
I originally thought that they would have to follow the same circle, but when I think about it this way it makes sense that the faster one would travel twice as far in the same time.
Let me know what you think.
Nope.
I think your diagram is flawed. If the planes turned like you said, 30 degrees for every 1 second, then the diagrams make sense. Since the plane is constantly turning however, a better approximation could be done by making the time interval smaller and smaller, to approximate an infinite amount of intervals. You assume that the change in angle of pitch is constant for both planes, i.e. both increasing by 60 degrees per second and taking 6 seconds to complete a 360 degree loop. I think the faster plane would have a greater change in it's pitch for the same amount of time.
The only way I can see the faster plane traveling a larger circle is if centrifugal force pushes the plane outwards, and then drag comes into play, not geometry.
different circle, but this is a pretty different question. you're limited in the amount of centripetal acceleration you can get because the steering wheel only turns so far and the tires only produce so much friction.
In case you haven't figured it out yet, the SPEED you travel, alone, does not tell you anything about the size of the circle. There are more parameters which you need to know.
Think of a racing oval. Different cars travel along it at different speeds, right? There is a winner and a loser, right? but they went the same distance, right?