Tethered Drone Cable Size, Voltage and Wind Catenary

The DC link has two equal copper conductors and a constant-power onboard converter. With $P_c=P_{load}/\eta_c$, the round-trip resistance is $R=2r_{20}k_R[1+\alpha_R(T_d-20\,^{\circ}\mathrm C)]L_{live}$. Solve $P_c=I(V_s-IR)$ using the stable, high-received-voltage root. Cable loss is $I^2R$; converter loss is $P_c-P_{load}$. This is the circuit in Beffert and Zell (2025), equations 2–8, with converter efficiency applied explicitly. Heating per cable metre includes both conductors: $q'=I^2r_{loop}$ and $\Delta T=q'R'_\theta$.

For minimum sending voltage, choose received voltage $U$ at least the converter cutoff, $\sqrt{P_cR}$, $\sqrt{P_cR(1-f)/f}$ and $P_c/I_{cap}$, then use $V_{s,min}=U+P_cR/U$. Here $I_{cap}$ is the smaller thermal and current-density limit. Bisection gives minimum electrical area and maximum live length. Voltage ratings are checked separately.

Mass is the sum of two copper areas, two insulation annuli, the strength member, a round outer-jacket annulus and additional specified mass. The core envelope holds the insulated conductor–strength member–insulated conductor arrangement in a straight row. NBS Handbook 100 supplies the copper-property basis; the built-in AWG table supplies area and resistance. Strength-member density defaults to typical aramid fiber; assembly stiffness and working loads are independent design inputs.

The cable uses Irvine’s extensible-cable equilibrium in unstretched arc coordinate $s_0$:

Weight is constant per unstretched metre, preserving mass. Normal wind drag per stretched metre follows the standard cross-flow formulation documented by Orcina: $\mathbf q_D=\tfrac12\rho C_DD|\mathbf V_\perp|\mathbf V_\perp$. It is converted to reference length using the elastic stretch. Damped Newton iterations solve endpoint compatibility, nested inside relaxed drag updates. Cumulative trapezoidal integration resolves the shape; no parabolic sag approximation is used.

Aircraft thrust balances its weight and drag plus the solved cable-end force. Along a vertical still-air proportional route, write $a=EA(h/L-1)$ and $b=wL/(2h)$. At trial height $H$, winch tension is $a-bH$, aircraft-end tension is $a+bH$, and required thrust is $W+a+bH$. The winch working load therefore imposes a lower height bound. Start above that bound, check feasibility, then refine the upper limit; loss of tautness bounds the route at $H=a/b$.

For other routes, search downward from maximum payout through height probes that include the entered operating height. If neighboring infeasible probes fail different constraints, bracket their individual crossings and test for a feasible interval between them. Refine the highest resolved feasible-to-infeasible bracket with 16 bisections, solving the elastic cable at every trial. Feasibility is not assumed to decrease from zero height. Independent published level and inclined cable cases from Li, Huang and Chen validate the common equilibrium solver.

Steady hover in the vertical plane containing the horizontal wind and downwind aircraft offset. Uniform air density and mean wind, circular cable drag diameter, constant normal drag coefficient, negligible axial skin friction and aerodynamic lift. Two copper conductors share equal current and have uniform design temperature.

Linear elastic cable with constant assembly EA; bending stiffness, creep, termination compliance and thermal expansion are neglected. Stiffness and working loads must describe the complete terminated assembly. The strength member carries the specified axial stiffness through the measured assembly input; copper stiffness is not added again.

The construction dimensions, polymer density, extra mass, resistance allowance, thermal resistance and working loads are illustrative design inputs, not a manufacturer's cable specification. Copper is standard annealed material at 20 °C before temperature and resistance allowances. The equations are derived here from circuit laws, force equilibrium and Hooke's law; no private reference text was used.

The current shape uses 1,024 spatial intervals and each altitude trial 512. General route bracketing uses 32 height intervals, reduced to 16 when a maximum-payout trial exceeds a limit by more than a factor of two to keep high-wind cases responsive. The entered operating height and sign-changing individual constraint boundaries are tested too. A feasible island wholly between probes without a bracketed constraint crossing can remain unresolved; “No interval resolved” does not prove that every height is infeasible. The vertical still-air branch uses its exact winch-load lower bound, including intervals narrower than the height-probe spacing.

Upper boundaries receive 16 bisections, giving height resolution no worse than the cable-limited route height divided by 65,536. A 512/1,024-interval tension comparison and independent force balance are checked. Strongly slack or near-zero-tension shapes may need finer spatial resolution; convergence conditions withhold nonconverged results. The altitude search has lower spatial resolution than the displayed operating shape, so very localized curvature or contact can shift the limiting height. No dynamics or played animation is implied.

The design conductor temperature is a conservative resistance basis, not a coupled electrothermal solution. Predicted temperature must not exceed that basis or the cable limit. Thermal resistance must include the worst reel, insulation and ambient cooling conditions; this is not an installation ampacity table. Nominal AWG solid diameter neglects strand voids, and the geometric mass/diameter model must be checked against the cable assembly.

Available thrust is an independent measured limit at the entered power. This tool does not predict a motor/propeller power–thrust curve or increase input power automatically as tether load changes. Maximum altitude retains that power budget and the current offset/height and unstretched-length/height ratios; it does not cover an arbitrary flight route, atmospheric ceiling, legal flight limits or emergency reserve.

Use manufacturer DC ratings for the actual insulation, connectors and converter, including no-load input voltage. Ground supply conversion loss, supply current limiting, switching transients and fault protection are outside the model. Steady loads do not establish gust strength, fatigue life or control stability. Check working loads, thermal behavior and electrical installation against the standard in force.

The metric/US switch converts supported inputs, results, chart axes and table columns. Drawing callouts retain their marked SI units. A vertical tether in still air must remain taut at the winch; the altitude route stops at zero winch tension.