Equilibrium Cable Configuration Estimation for Aerostat Using Approximation Method
This paper presents estimation technique for equilibrium cable parameters applicable to aerostat balloon. The direct integration expressions are first expressed for uniform wind speed and density with height. Two types of polygonal approximations are then
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Abstract This paper presents estimation technique for equilibrium cable parameters applicable to aerostat balloon. The direct integration expressions are first expressed for uniform wind speed and density with height. Two types of polygonal approximations are then derived for numerical estimation which can directly be applied to varying wind speed as well as air density with height. A comparison of polygonal approximations is then carried out with direct integration for a small size aerostat assuming uniform wind speed and air density with height. Then the polygonal approximation is applied to a medium size aerostat considering the air density variation with height and thereby proposing a tether length factor for aerostat design. Finally, the method is applied for a practical case of both wind speed and air density variation with height. The results suggest that with a reasonable number of elements, the polygonal approximations can successfully be applied for estimation of equilibrium cable parameters for the aerostat balloon. Keywords Tether cable
Polygonal approximation Tether length factor
List of symbols B CD ; CL CDc dc
Buoyancy force Drag and lift coefficients Tether cable drag coefficient Tether cable diameter
A. Kumar (&) S.C. Sati Aerial Delivery Research & Development Establishment, Agra 282001, India e-mail: [email protected] S.C. Sati e-mail: [email protected] A.K. Ghosh Department of Aerospace Engineering, Indian Institute of Technology, Kanpur, Kanpur 208016, India e-mail: [email protected] © Springer Science+Business Media Singapore 2016 M. Pant et al. (eds.), Proceedings of Fifth International Conference on Soft Computing for Problem Solving, Advances in Intelligent Systems and Computing 437, DOI 10.1007/978-981-10-0451-3_82
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DA dl g l L LA nd p S
Aerodynamic drag force Small/polygonal cable element Acceleration due to gravity Tether cable length from anchor point Total tether cable length Aerodynamic lift force Cable drag per unit length for cable normal to the wind wc =2n 2=3 Characteristic area of balloon, Vb Tensions of tether cable at lower and upper ends, respectively Steady wind velocity Volume of balloon hull (i.e., gas bag) Structural weight of balloon (including bridle, payload, and test instruments) Tether cable weight per unit length Coordinates on tether cable w.r.t. anchor point Coordinates of balloon confluence point with respect to tether cable anchor point Trim angle of attack and sideslip angle Angle between nth cable element and horizontal Angles between the horizontal and tether cable at lower and upper ends Atmospheric air density at height Helium density s at lower and upper ends, respectively, of tether cable
T0 ; T1 V1 Vb WS wc x; z x1 ; z 1 a dn c0 ; c1 qh qg s0 ; s1
1 Introduction Aerostats are lighter than air systems, usually filled with helium gas and are tethered to the ground. They provide useful platform for payload mounting due to increased line of sight. There are many advantages of using aerostat platforms, some of which are lon
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