Dumb physics question

[Sarevok]

Consider a spacecraft such as the american space shuttle. In order to reach orbit it has to reach a velocity of approximately 8000 meters per second.

Now consider a bog standard aircraft travelling at 200 meters per second. It makes 40 u-turns. The total velocity change adds upto 8000 meters per second.

Question 1. Can any aircraft actually make 40 u turns with total velocity change of 8000 meters per second and yet have fuel remaining ?

Question 2. If so then how is this possible ? How can aircraft make such great velocity changes when it takes a rocket of huge size to do the same ?

[Kuroneko]

An aircraft capable of forty u-turns to 200m/s wouldn't be capable getting to 8000m/s, as aerodynamic drag makes the requisite engine thrust about 1600 times as much.

But to answer your not-so-dumb question, due to the presence of air, making a u-turn is actually much easier than turning around and firing the engines in the opposite direction, as the aircraft can push against the air to change its direction. When it banks, there is a difference between the lift-induced drags generated by the wings, and that, along with the rudder, what turns the plane. So rather than thinking of Δv's stacking on each other, think of it as a plane going with a set speed changing direction basically for 'free'. This should be more clear if you imagine the plane going in a circle several times instead: the velocity vector is always perpendicular to the centripetal force, so the work done against it is zero.

No doubt the above contains a certain amount of idealization; I'd be interested in knowing to what extent actual aircraft deviate from it.

[Batman]

Since 40 u-turns essentially DO amount to flying in a circle 20 times, not all that much I think.
Assuming a circle diameter of 10 km which at 200mps or 720 kph amounts to a pretty mellow turn even for civilian aircraft for 20 complete circles that gives us a travel time of 3141.6 seconds/52.35 minutes, easily within the endurance envelope of many small private aircraft.
Whereas if you look at the thrust-to-weight-ratio of even the most modern fighter aircraft (which determines how much of a brute-force velocity change the can actually achieve, which is what you have to do if you want to get to orbit) they're hard-pressed to maintain a sustained vertical climb even with minimal combat loads and have an endurance measured in minutes doing it.

[Sea Skimmer]

Consider a spacecraft such as the american space shuttle. In order to reach orbit it has to reach a velocity of approximately 8000 meters per second.

Now consider a bog standard aircraft travelling at 200 meters per second. It makes 40 u-turns. The total velocity change adds upto 8000 meters per second.

Apples and oranges. Total velocity change is not a very useful measure of relative aerospace craft performance. If I personally ran in circles long enough I could have a total velocity change that big too. It doesn’t mean I can fly (at least not without that NASA pedal powered airplane and years of physical conditioning to pedal it) or reach space either.

Question 1. Can any aircraft actually make 40 u turns with total velocity change of 8000 meters per second and yet have fuel remaining ?

Just about any decent conventional air breathing aircraft could do that and far more.

Question 2. If so then how is this possible ? How can aircraft make such great velocity changes when it takes a rocket of huge size to do the same ?

The shuttle is employing liquid rocket motors and two big solid rocket boosters to overcome gravity to reach orbit, creating a tremendous amount of potential energy in the process expressed in its final massive speed. That potential energy will be converted into the heat of reentry when the shuttle returns. All fuel and oxidizer is carried on board from liftoff to orbit.

A plane making a turn is not increasing its potential energy when it changes velocity in a turn, it’s just steadily converting its thrust energy into lift energy which is lost as drag (causing a slight skin heating effect, though this can become very considerable on a supersonic jet), and any typical aircraft is employing an air breathing engine. Rocket planes are rare and very short ranged. That means for every pound of fuel the air breathing aircraft carries, it burns about 14lbs of oxygen it sucked out of the air as it went along. The shuttle had to carry all 15lbs of fuel and oxidizer with it because air breathing engines won’t work at the massive heights it climbs too. The shuttle design is also just rather inefficient in general; it was poorly designed and produced on a lean budget for reusability, not fuel economy.

Furthermore air breathing engines, be they jets or propeller types, are inherently more efficient then rocket engines because they accelerate a larger mass of propellant (the surrounding air) to a low speed. A rocket motor works by accelerating a relatively small mass of propellant to extremely high speed. This difference is defined by an engines specific impulse.

Spaceship One and Spaceship Two combined technologies, by using a air breathing jet turbine powered first stage aircraft to transport a liquid fuel rocket powered spacecraft to about 50,000 feet and then release it. This allows the rocket stage to be far smaller then if it was launched from sea level. Some satellites are also orbited by air launching a booster rocket.

[starslayer]

There is no net velocity or speed change in the problem. After a plane has made 40 u-turns, it will be facing exactly the way it was before, still going 200 m/s, meaning there has been no net change in velocity (remember, velocity is a vector, and speed is always a positive scalar). Kuroneko already noted this in the last sentence of his explanation.