A longitudinal air–water trans-media dynamic model for slender vehicles under low-speed condition

  • Zongcheng MaEmail author
  • Junhua Hu
  • Jinfu Feng
  • An Liu
  • Guoming Chen
Original paper


A trans-media aerial underwater vehicle (TMAUV) could break through the single-medium limitation with the abilities to fly in the air, navigate underwater, and cross the air–water surface repeatedly. This paper researches on the air–water trans-media trajectory, including the water entry and exit trajectories, for slender TMAUVs. A longitudinal dynamic model is developed for the air–water trans-media process under low-speed condition. In this condition, the vehicle is assumed to be fully wetted and the water surface is assumed to be kept flat. A novel estimation for the fluid force is proposed for the immersed part of the vehicle, with angular velocity and angle of attack taken into consideration. Added mass and its derivatives are calculated by the cross-sectional method based on the slender body theory. To verify the feasibility and effectiveness of the model, water entry experiments of a slender projectile with a length of 2000 mm are performed with ground and underwater high-speed cameras. Simulations and experimental results show similar trends, as indicated by the comparisons. Furthermore, the proposed model is compared with computational fluid dynamics method simulating water entry and exit processes. Simulation results present good agreement with experimental results. On the basis of the results, the proposed model could be used to predict the water entry and exit trajectories with different initial conditions.


TMAUV Water entry Water exit Slender body theory Cross-sectional method 



The authors would like to thank all technicians of Northwestern Polytechnical University for their help in the experimental setup. Project supported by the National Natural Science Foundation of China (Grant No. 51779263).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Zongcheng Ma
    • 1
    Email author
  • Junhua Hu
    • 2
  • Jinfu Feng
    • 2
  • An Liu
    • 2
  • Guoming Chen
    • 2
  1. 1.School of Aviation Operations and ServicesAviation University of Air ForceChangchunChina
  2. 2.Aeronautics Engineering CollegeAir Force Engineering UniversityXi’anChina

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