How are gravitational losses on ascent related to horizontal velocity?

2018-06-22 15:07:31

Loren Petchel wrote:

gravity loss is 9.8m/s * (1 - your fraction of orbital speed) so you want to build horizontal speed as soon as it won't cost you too much drag.

My "feel" in Kerbal Space Program tells me otherwise. A low-TWR upper stage (order of TWR 0.3) is doomed to plunge into the atmosphere if it's missing 1/4 of its orbital velocity, even if burning at an angle "upwards". Actual reduction of gravitational drag "feels" to be non-linear, only last 200-300m/s out of Kerbin's 2200m/s really changes things. This is just a subjective feel in a quite inaccurate space simulator. How is it for real? Is Loren's equation accurate or is my "feel" supported by actual hard maths?

Since "gravitational losses" is a rather loose term with no firm definition, let's introduce a term (already common in the Kerbal Space Program community) which allows quantifying them well: gravitational drag.

Gravitational drag can be understood as weight of a body in motion over planet

  • Since "gravitational losses" is a rather loose term with no firm definition, let's introduce a term (already common in the Kerbal Space Program community) which allows quantifying them well: gravitational drag.

    Gravitational drag can be understood as weight of a body in motion over planet's surface, adjusted for centripetal acceleration caused by motion relative to the planet's curvature. For immobile craft it will be its weight; for a craft in circular orbit it's zero.

    Gravitational drag is an especially handy tool for calculations regarding spaceplanes - since it's the force directly counteracted by airplane's lift, it makes a very natural appearance in equations regarding spaceplane aerodynamics, in place where airplane equations use weight.

    For rockets, it's offset by the vertical component of thrust, and rocket's total delta-V wasted on fighting gravitational drag is directly proportional to value of the gravitational drag and time spent under its influence; that way it's a

    2018-06-22 15:21:29