Study of the stability of motion in water of amphibious wheeled transport and technological units in the hydroplaning mode

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Abstract

BACKGROUND: Amphibious wheeled transport and technological units (AWTTU) are critically important for rescues and other special operations, but their velocity in water is limited due to high wheel resistance and suboptimal hydrodynamics. Existing studies do not take into account the hydroplaning mode in a comprehensive manner.

AIM: Development of a mathematical model of the motion in water of an amphibious vehicle in the hydroplaning mode, which takes into account both hydrostatic and hydrodynamic forces.

METHODS: Equations for determining excess pressure on the hull surface are derived based on the Cauchy-Lagrange integral, a calculation scheme for the interaction of a flat-bottomed hull with the water surface is developed. Analytical expressions for the lifting hydrodynamic force, resistance force, and hydrodynamic moment are obtained. An analysis of the stability of motion is carried out taking into account the position of the center of gravity, the magnitude of the traction force of the watercraft propeller, and the trim angle.

RESULTS: It was found that at Froude numbers Fr > 3.0, hydrodynamic forces ensure 95–97% of sustaining the AWTTU afloat. The criteria for the motion stability are obtained: with a negative arm of the propulsion force, the stability depends on the magnitude of the thrust, with a positive arm, the critical speed of motion is determined. It was found that the thickness of the “reverse jet” is proportional to the angle of attack, the resistance force has a quadratic dependence on the velocity, the arm of the hydrodynamic moment is linearly dependent on the trim angle.

CONCLUSION: The developed mathematical model allows analyzing the motion of the AWTTU in the hydroplaning mode taking into account key hydrodynamic factors. The obtained results create a theoretical basis for the design of high-velocity amphibious vehicles and require further experimental validation.

About the authors

Oleg A. Kozelkov

Moscow Polytechnical University

Email: kozelkow@mail.ru
ORCID iD: 0009-0009-4163-3721
SPIN-code: 8140-1200

Dr. Sci. (Engineering), professor, Head of the Scientific and Technical Center «Automated Technical Systems»

Russian Federation, Moscow

Mikhail M. Zhilejkin

Moscow Polytechnical University

Email: jileykin_m@mail.ru
ORCID iD: 0000-0002-8851-959X
SPIN-code: 6561-3300

Dr. Sci. (Engineering), professor, Senior researcher at the Scientific and Technical Center «Automated Technical Systems»

Russian Federation, Moscow

Timur V. Kondratenko

Moscow Polytechnical University

Email: Timur-150@mail.ru
ORCID iD: 0009-0003-6405-6556
SPIN-code: 1219-0733

Postgraduate of the Land Vehicles Department

Russian Federation, Moscow

Vsevolod A. Neverov

Moscow Polytechnical University

Author for correspondence.
Email: sevasxp@mail.ru
ORCID iD: 0000-0003-0515-9785
SPIN-code: 4896-2213

Cand. Sci. (Engineering), Senior researcher at the Scientific and Technical Center «Automated Technical Systems»

Russian Federation, Moscow

References

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2. Fig. 1. Calculation scheme of motion of the amphibious wheeled transport and technological unit afloat in a hydroplaning mode: C, center of gravity of the amphibious wheeled transport and technological unit; D, center of gravity of the immersed part of the hull of the amphibious wheeled transport and technological unit; X, Y, Z, axes of the moving reference frame; X2, Y2, Z2, axes of the fixed reference frame; φ, trim angle; α, angle between direction of the vector of thrust of a water propulsion unit and the X-axis of the moving reference frame; l, length of wetted surface of the hull; b, distance between the center of gravity of the amphibious wheeled transport and technological unit and the hull end; hB, arm of the vector of thrust of a water propulsion unit; dS, differential area; lа, arm of hydrostatic force; FB, thrust force of the water propulsion unit; FА, hydrostatic force; R0, lifting force caused by oncoming water flow; Rx, resistance force of motion in water; M0, hydrodynamic moment; ∆p, excess pressure acting at a differential area of the hull of the amphibious wheeled transport and technological unit; Mg, weight of the amphibious wheeled transport and technological unit; v, possible water rate; ωy, angular velocity of trim oscillations of the amphibious wheeled transport and technological unit.

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3. Fig. 2. Calculation scheme of the interaction of the amphibious wheeled transport and technological unit bottom with water flows: φ, inclination angle of the plate; v0, oncoming flow rate; δ, oncoming flow thickness; R0, lifting force; l, distance between the rear edge to the tangent to the free surface perpendicular to the plate; X, Z, axes of the moving reference frame; X2, Z2: axes of the fixed reference frame; Rx, resistance force; M0, hydrodynamic moment; O1, wave amplitude; h2, arm of the lifting force.

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4. Fig. 3. Direction of the force vector of the water propulsion unit, in which the force arm is less than zero: X, Z, axes of the moving reference frame; hB, arm of thrust force vector of the water propulsion unit; FB, thrust force of the water propulsion unit; α, angle between direction of the thrust vector of the water propulsion unit and the X-axis of the moving reference frame.

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5. Fig. 4. The two-axle amphibious wheeled transport and technological unit moving in hydroplaning mode: a, entering the water; b, damping of transient processes; c, acceleration; d, transition to the hydroplaning mode.

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6. Fig. 5. Trim angle of the two-axle amphibious wheeled transport and technological unit when moving in hydroplaning mode.

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7. Fig. 6. Position of the center of gravity of the amphibious wheeled transport and technological unit during motion.

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8. Fig. 7. Immersion level of the center of gravity of the amphibious wheeled transport and technological unit.

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9. Fig. 8. Motion velocity of the amphibious wheeled transport and technological unit.

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10. Fig. 9. Thrust force of the watercraft propulsion unit.

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11. Fig. 10. Change in hydrostatic lifting force.

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12. Fig. 11. Change in hydrodynamic lifting force.

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13. Fig. 12. Change in hydrodynamic moment.

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14. Fig. 13. Loss of capsizing stability of the two-axle amphibious wheeled transport and technological unit relative to the transverse axis

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15. Fig. 14. Trim angle at capsizing.

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16. Fig. 15. Graphical solution (20) for a fixed value of the force Fв: vmax, maximum speed for the adopted value of Fв.

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17. Fig. 16. Direction of the force vector Fв of the water propulsion unit, at which hв is greater than zero: X, Z, axes of the moving reference frame; hB, arm of thrust force vector of the water propulsion unit; FB, thrust force of the water propulsion unit; α, angle between direction of the thrust vector of the water propulsion unit and the X-axis of the moving reference frame.

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18. Fig. 17. Transient processes for the trim angle φ have the shape of a damped sinusoid.

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