Fighter Jet and Curvature of the earth

The average curvature of the earth is 7.98 inches per mile. So it would be1596 inches (133’) in 200 miles.

Let we have 400 miles perfectly or ideal leveled runway. A fighter jet starts its journey from one end of the runway and increases Its speed till it reaches to a maximum speed of 2500 km/h (or increases its speed beyond the limit which requires for its flying in the air) in the first stretch of 1 or 2 miles from the starting end. So will this jet lift off the ground automatically in air due to a curvature of the earth?

The said jet takes off in a normal way. After few minutes it turns its nose upward and shoots straight vertically up into the sky. This jet is now making 90 degrees vertical angle with the tangent of curvature of the earth just below it. After some time, the pilot decides to fly on the imaginary line in an airspace, which is parallel to the above tangent. So he abruptly turns its nose down (90 degrees) and starts flying on his desired line in the airspace. So will this jet gain elevation if fly for 100 miles on the same said line? 

The average curvature of the earth is 7.98 inches per mile. So it would be1596 inches (133’) in 200 miles.

Let we have 400 miles perfectly or ideal leveled runway. A fighter jet starts its journey from one end of the runway and increases Its speed till it reaches to a maximum speed of 2500 km/h (or increases its speed beyond the limit which requires for its flying in the air) in the first stretch of 1 or 2 miles from the starting end. So will this jet lift off the ground automatically in air due to a curvature of the earth?

No

The said jet takes off in a normal way. After few minutes it turns its nose upward and shoots straight vertically up into the sky. This jet is now making 90 degrees vertical angle with the tangent of curvature of the earth just below it. After some time, the pilot decides to fly on the imaginary line in an airspace, which is parallel to the above tangent. So he abruptly turns its nose down (90 degrees) and starts flying on his desired line in the airspace. So will this jet gain elevation if fly for 100 miles on the same said line?

Yes

The average curvature of the earth is 7.98 inches per mile. So it would be1596 inches (133’) in 200 miles.

Let we have 400 miles perfectly or ideal leveled runway. A fighter jet starts its journey from one end of the runway and increases Its speed till it reaches to a maximum speed of 2500 km/h (or increases its speed beyond the limit which requires for its flying in the air) in the first stretch of 1 or 2 miles from the starting end. So will this jet lift off the ground automatically in air due to a curvature of the earth?
The said jet takes off in a normal way. After few minutes it turns its nose upward and shoots straight vertically up into the sky. This jet is now making 90 degrees vertical angle with the tangent of curvature of the earth just below it. After some time, the pilot decides to fly on the imaginary line in an airspace, which is parallel to the above tangent. So he abruptly turns its nose down (90 degrees) and starts flying on his desired line in the airspace. So will this jet gain elevation if fly for 100 miles on the same said line?

Holy cow!  Takeoff speed is usually about 150 knots (≈275 km/h).  They can't go much faster than that without lift off.  It takes aircraft 300 ft to reach that speed on an carrier.  It's about 1500 ft without the catapult.

The speed of 2470 km/h is Mach 2 supersonic speed.

Curvature of the Earth was approximated to 7.98 or 8 inches per mile squared.
It means after 2 miles is 2² * 8 , not 2 * 8.

Airplanes rely on wing lift.
Upward force depends on size and shape of the wing and on air speed and density at different altitudes.
To keep altitude, the upward force should counter plane weight equally.
If plane goes little up, air gets a bit thinner and upward force decreases.
If plane goes down, air gets a bit thicker and upward force increases.

If we ignore dependency on air lift and weight fall, and allow our imaginary jet to fly in straight lines, then yes.

After 3 miles plane will be in air by 3² * 8 = 72 inches (6 ft).
After 6 miles it will be 6² * 8 = 288 in (24 ft).
After turning straight up, gaining altitude and turning back horizontally, it will continue gaining additional altitude at the same rate.
25 miles from the origin it would be 25² * 8 = 5000 in, or 416.66 ft, plus altitude gain on 90 degrees upward flight.

But you already know that in real life airplanes need balance between air lift and weight to operate.

400 mile runway??

400 mile runway??

It's a thought experiment. Just not a particularly well-thought-out one.

Quote from: Here to laugh at you on January 26, 2018, 02:03:55 PM

400 mile runway??

It's a thought experiment. Just not a particularly well-thought-out one.

I suppose he could be experimenting with this new thing called "thought"...

How about if the said jet takes off the ground @ an angle of 27 degrees, gains height and then goes down (same angles) back to horizontal. Will this jet also gain additional altitude if flying horizontally (27-27=0)? Just yes or no are fine – Many Thanks

How about if the said jet takes off the ground @ an angle of 27 degrees, gains height and then goes down (same angles) back to horizontal. Will this jet also gain additional altitude if flying horizontally (27-27=0)? Just yes or no are fine – Many Thanks

The key word being "horizontally", no. It should not gain altitude.

I mean the pilot bring back his jet to the previous horizontal line - 27 degrees minus 27 degrees

How about if the said jet takes off the ground @ an angle of 27 degrees, gains height and then goes down (same angles) back to horizontal.

A jet that takes off at an angle of +27 degrees, gains altitude, and then changes angle by -27 degrees will not be flying horizontally.

After flying for 1600 km, then increasing pitch by 27 degrees, then flying another 1600 km, then reverting pitch back by 27 degrees,
the plane will fly parallel to original horizontal, bit not with destination horizontal.

(If after 3200 km pilot wants to fly horizontally, he will have to revert pitch for more than 27 degrees.)



Meanwhile artificial horizon in the plane will gradually self-correct to every local horizontal on the way and show that the flight is not horizontal.
If pilot follows artificial horizon to keep the pitch (and in real life he does), his both 1600 km segments will curve,
according to all new inclinations of local horizontals at new positions.
Final segment will also keep curving routinely.
His reference is tied to ground, not to some imaginary tangential plain.

It is much harder to follow actual straight lines, because he would have to calculate constantly corrections away from artificial horizon.