Acceleration with unknown time

[Tembaco]

I just took a physics test and I couldn't get my head around one of the questions. Even though I think I understand it I don't not know the answer for sure. It has been bothering me ever since I got home so I hope one of you guys can put me out of my misery. The question goes (from the top of my head):

Airplane carrier

An jetfighter going 220 km/h lands on a aircraft carrier and stops quickly with the assistance of an arresting hook.

At the instance the wheels touch the deck there is 200m of runway left.

It takes 0.20 seconds before the hook catches a rope and the plane comes to a standstill with just 13.1m of runway left.

A. Calculate the deceleration of the plane

B. Draw a graph(v,t) and calculate how long it takes for the plane to stop

I am not only looking for an answer! Please also tell me how you did it.

Thanks in advance.

[drakesdoom]

You have 200m of deck on touchdown.

You were going 220km/h for .2 seconds of that 200m

Then you catch and stop with 13.1m left.

Look at it like that and you can get the distance, starting speed, final speed is 0. Just a bit off math to finish it off.

[K^2]

When either your final or initial velocity is zero, the shortcut for relating velocity to distance and acceleration, assuming acceleration is constant, is v² = 2ad.

[Tembaco]

v² = 2ad.

I did the right thing then. Thanks

Edited October 23, 2013 by Tembaco

[Mr Shifty]

Problem of course neglects the fact that the pilot goes to full power as soon as the wheels hit the deck so that she can take off again if she misses the wire. So probably an initial period of acceleration before the deceleration. Then, you could probably model the arresting wire as a spring (to a first approximation), which has a force proportional to its deflection from rest, which means the deceleration would actually not be constant, but would ramp up (sinusoidally) over the time of the stop.

[PakledHostage]

the deceleration would actually not be constant, but would ramp up (sinusoidally) over the time of the stop.

Rate of change of acceleration with respect to time... I always thought that'd make a good custom license plate if you could find a way to fit it in. Especially for an SUV.

[GoDores]

Rate of change of acceleration with respect to time... I always thought that'd make a good custom license plate if you could find a way to fit it in. Especially for an SUV.

XS DVDT

6 letters. Fits on any plate. Better for a sports car than an SUV IMHO.

(Technically yours would be XS DADT, but when has jerk been a big measure of auto performance?)

[PakledHostage]

but when has jerk been a big measure of auto performance?)

I was going with the stereotype about the guy in it.

[K^2]

Then, you could probably model the arresting wire as a spring

Nah. An arresting wire really is closer to a constant. At least, that is the goal. The wire is connected to a hydraulic system which is governed by a relieve valve set to a particular pressure. So deceleration builds up quickly to a target level and remains roughly constant.

[Camacha]

Nah. An arresting wire really is closer to a constant. At least, that is the goal. The wire is connected to a hydraulic system which is governed by a relieve valve set to a particular pressure. So deceleration builds up quickly to a target level and remains roughly constant.

That would make sense from a theoretical point of view too. To have the least chance of mechanical failure it makes sense to have the same (smooth) decelaration until a full stop has been achieved. Spikes, jerks or peak loads would result in failure at that point, or would cause the parts having to be overdimensioned.

[PakledHostage]

Don't completely discount Mr Shifty though... I recall from some of his other posts that he served aboard at least one US aircraft carrier.

[K^2]

Don't completely discount Mr Shifty though... I recall from some of his other posts that he served aboard at least one US aircraft carrier.

In this particular case we should. The main design goal of the arrester system is to bring an aircraft down to a stop in a fixed distance under minimum stress, while allowing for maximum opportunity for safe abort. Linear force is not quite the worst thing you could do here, but it's very far from the best. Even using spring-and-pulley systems you can do much, much better. But hydraulics are used specifically because they give you the closest thing to constant, adjustable force.

[Mr Shifty]

If you ask me questions about the reactor plants or damage control systems or managing the bridge, I would be a more reliable source. (Though it's been 10 years.) I have (had?) only cursory knowledge of flight deck equipment. I'm sure K^2 is right here; my speculation was just that.

[PakledHostage]

I'm sure K^2 is right here; my speculation was just that.

If feels a bit funny to defend my defence of another forum member to the forum member I was defending, but I was thinking of this quote when I posted above:

Problem of course neglects the fact that the pilot goes to full power as soon as the wheels hit the deck so that she can take off again if she misses the wire. So probably an initial period of acceleration before the deceleration.

That part, to the best of my knowledge, is correct. This is done as a precaution because it would take the pilot and engines too long to respond after the pilot recognized that they'd missed the hook. You can see and hear them doing it in the videos.

[Mr Shifty]

That part, to the best of my knowledge, is correct. This is done as a precaution because it would take the pilot and engines too long to respond after the pilot recognized that they'd missed the hook. You can see and hear them doing it in the videos.

Oh yes, that part is undoubtedly correct. Having stood on the bridge for many many takeoffs and landings, I can assure you that landings are far louder because the planes go to full throttle when they land. They actually miss the wires quite often: say 5-10% of the time for seasoned pilots, more than 50% for the RAGs. I remember a particular time when an F-18 came down silently and (luckily) caught the wires. There was complete silence over the radio for several seconds before the Air Boss (O-6 in charge of carrier flight ops) came on the line and said "101 (or whatever the call sign was), never ever do that again."

[drakesdoom]

It was my understanding that reaction time would not matter as the jets cannot spool up fast enough to perform a go around if they were throttled down to land even given no reaction time involved.