Next Article in Journal
On the Wake Properties of Segmented Trailing Edge Extensions
Next Article in Special Issue
Leading-Edge Roughness Affecting Diamond-Wing Aerodynamic Characteristics
Previous Article in Journal
Cost-Effectiveness of Structural Health Monitoring in Fuselage Maintenance of the Civil Aviation Industry
Previous Article in Special Issue
Flight Load Assessment for Light Aircraft Landing Trajectories in Windy Atmosphere and Near Wind Farms
Article Menu
Issue 3 (September) cover image

Export Article

Open AccessArticle
Aerospace 2018, 5(3), 88;

On Four New Methods of Analytical Calculation of Rocket Trajectories

CCTAE, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
These authors contributed equally to this work.
Author to whom correspondence should be addressed.
Received: 15 June 2018 / Revised: 20 July 2018 / Accepted: 27 July 2018 / Published: 15 August 2018
(This article belongs to the Collection Feature Papers in Aerospace)
Full-Text   |   PDF [469 KB, uploaded 19 August 2018]   |  


The calculation of rocket trajectories is most often performed using purely numerical methods that account for all relevant parameters and provide the required results. There is a complementary need for analytical methods that make more explicit the effect of the various rocket and atmospheric parameters of the trajectory and can be used as test cases with unlimited accuracy. The available analytical methods take into account (i) variable rocket mass due to propellant consumption. The present paper includes four new analytical methods taking into account besides (i) also (ii) nonlinear aerodynamic forces proportional to the square of the velocity and (iii) exponential dependence of the mass density with altitude for an isothermal atmospheric layer. The four new methods can be used in “hybrid analytical-numerical” approach in which: (i) the atmosphere is divided into isothermal rather than homogeneous layers for greater physical fidelity; and (ii) in each layer, an exact analytical solution of the equations of motion with greater mathematical accuracy than a numerical approximation is used. This should allow a more accurate calculation of rocket trajectories while discretizing the atmosphere into a smaller number of layers. The paper therefore concentrates on four analytical methods of calculation of rocket trajectories in an isothermal atmospheric layers using new exact solutions of the equations of motion beyond those currently available in the literature. The four methods are developed first for the simpler case of a vertical climb and will be subsequently extended to the practically more relevant case of a gravity turn. View Full-Text
Keywords: rocket trajectories; analytical methods; variable mass; nonlinear aerodynamic forces; atmospheric stratification rocket trajectories; analytical methods; variable mass; nonlinear aerodynamic forces; atmospheric stratification

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Campos, L.M.B.C.; Gil, P.J.S. On Four New Methods of Analytical Calculation of Rocket Trajectories. Aerospace 2018, 5, 88.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Aerospace EISSN 2226-4310 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top