### Author Topic: Trajectories of recent satellite launches  (Read 473 times)

#### bknight

• Uranus
• Posts: 2427
##### Trajectories of recent satellite launches
« on: March 19, 2017, 03:01:52 PM »
I watched the ULA launch yesterday and noticed that the trajectory reached ~270 miles and then the pitch was changed so the altitude decreased to ~ 200 miles while velocity continued to increase.  I remember several that had similar profiles.
I have done a lot of review of Bob. B's Saturn launch simulator and that trajectory was up and then "flat until orbital velocity was achieved.

My question is why this profile is planned and carried out with more current launches?
Truth needs no defense.  Nobody can take those footsteps I made on the surface of the moon away from me.
Eugene Cernan

#### Peter B

• Jupiter
• Posts: 708
##### Re: Trajectories of recent satellite launches
« Reply #1 on: March 20, 2017, 08:11:37 AM »
I don't know the maths of it, but I'll have a couple of guesses.

1. Any altitude gained above the intended orbital altitude (that is, the climb from 200 miles to 270 miles) represents potential energy that can be cashed in for speed when the rocket dives back down to orbital altitude. My guess is that this potential energy is more cheaply gained when the rocket is going more slowly, and more efficiently spent when the rocket is going faster.

2. By climbing to the higher altitude the rocket is able to gain speed more efficiently by encountering less drag. Because drag increases at the square of the speed (or something like that), the high speed of a rocket means that even at orbital altitudes there are efficiencies to be gained by climbing even higher to where the atmosphere is even thinner.

How did I go?

#### bknight

• Uranus
• Posts: 2427
##### Re: Trajectories of recent satellite launches
« Reply #2 on: March 20, 2017, 08:36:42 AM »
Yes, I thought about the gain of kinetic energy aided by Earth's gravity.  The drag may or may not be accurate the difference in drag at 200 miles seems to be small compared to 270 miles.
I don't know the maths either, so my perception may be way off, and that is why I asked the question.
Truth needs no defense.  Nobody can take those footsteps I made on the surface of the moon away from me.
Eugene Cernan

#### Obviousman

• Mars
• Posts: 329
##### Re: Trajectories of recent satellite launches
« Reply #3 on: March 20, 2017, 04:12:57 PM »
The potential energy gain proposition seems reasonable. We certainly do that with aircraft a lot (climb to slightly above desired altitude then descend to pick up speed before trimming out).

#### QuietElite

• Venus
• Posts: 36
##### Re: Trajectories of recent satellite launches
« Reply #4 on: May 13, 2017, 10:35:25 AM »
Some rockets have upper stages with a very low thrust-to-weight ratio, so they get boosted up higher by the lower stage to have more time to gain velocity and to get into orbit.

#### ka9q

• Neptune
• Posts: 2841
##### Re: Trajectories of recent satellite launches
« Reply #5 on: May 17, 2017, 04:46:16 AM »
Launch vehicle trajectory optimization is a complicated subject, and I can't say I fully understand it. But I can list some of the important considerations.

Atmospheric drag is a big consideration in first-stage flight from the earth's surface. You obviously want to reduce it by getting above the thickest parts of the atmosphere as soon as possible.

Gravity losses are another big consideration in first-stage flight. Except at a pitch angle of zero (i.e., the launch vehicle is horizontal) some of its thrust goes to counteracting gravity rather than accelerating the launch vehicle. Gravity losses are clearly a maximum at liftoff when the launcher is pointed straight up and is still full of unburned propellant. To minimize gravity losses you a) use the highest thrust-to-weight ratio you can afford (which is why large solid rocket boosters are so popular) and b) reduce the pitch angle as quickly as possible. Obviously you can't do this too quickly or the rocket will fall back onto the ground!

At liftoff the engines must support the rocket's entire weight as well as accelerate it to orbit, but as you accelerate downrange the earth will begin to fall away from you due to its curvature, leaving less of the rocket's weight to be supported by upward rocket thrust. (Once you're in orbit, then by definition no upward supporting thrust is needed, as the earth is now falling away from you at least as quickly as you free-fall toward it.)

I.e., you obviously want to build downrange velocity as quickly as you can, but this is also at odds with gaining altitude as quickly as possible to get out of the thicker air near the ground, especially before you build up much velocity.

This calls for the classic curved trajectory that begins by going straight up from the launch pad to gain altitude and then progressively pitching down toward the horizontal as you pick up velocity.

The aerodynamic forces on the rocket depend on both its velocity and the density of the surrounding air, so as the rocket accelerates into thinner air these forces reach a peak and then decrease to zero. This "Max-Q" peak usually occurs between 60 and 90 seconds after liftoff, and the forces can be so extreme that even a small non-zero angle of attack (the angle between the rocket's longitudinal axis and the relative wind) can produce a bending moment that tears the rocket apart. This is usually done with a maneuver called a "gravity turn", which lets gravity gradually bend the launch trajectory toward the horizontal while maintaining a near-zero angle of attack.

Controlling the angle of attack in the max-Q region is so critical that Apollo's Emergency Detection System automatically triggered an abort if the sensed angle of attack exceeded a safe threshold; waiting for the commander to do it manually could well be fatal.

#### bknight

• Uranus
• Posts: 2427
##### Re: Trajectories of recent satellite launches
« Reply #6 on: May 17, 2017, 09:58:37 AM »
Good discussion, but there isn't that much atmosphere at 240 miles and the rocket hasn't reached orbital speeds, yet.  The rocket(s) must pitch down as the velocity continues to increase as thee altitude decreases. Perhaps it is just using the Earth's gravity to finish acceleration to orbital velocity.  That is why I asked he question in the OP, none of the rocket scientists have weighed in to my knowledge.
Thanks for the input.
Truth needs no defense.  Nobody can take those footsteps I made on the surface of the moon away from me.
Eugene Cernan