Checking the fuse’s time-current curve (Admiralty Handbook, Plate 12), a 40 A fuse would clear 1285 A in ~0.01 seconds — safe. But the mechanical switch arced badly. Gibbs recommended adding a high-speed circuit breaker. Post-war, HMS Vigilant got new radar. The induction motor load (radar rotating aerial) had a power factor of 0.65 lagging . Apparent power S = 8 kVA, true power P = 5.2 kW. The generator ran hot.
Cable data: 16 mm² copper, length 30 m round trip. Resistance: [ R_{cable} = \rho \times \frac{L}{A} = 0.0175 \times \frac{60}{16} \approx 0.0656\ \Omega ]
Gibbs calculated required capacitive reactive power to raise PF to 0.90. examples in electrical calculations by admiralty pdf
For PF=0.90, new apparent power (S_2 = P / 0.90 = 5.2 / 0.90 \approx 5.78\ \text{kVA}) New reactive power (Q_2 = \sqrt{5.78^2 - 5.2^2} \approx 2.52\ \text{kVAR})
Then cable cross-section area (A): [ A = \frac{\rho \times L}{R} = \frac{0.0175 \times 45}{0.0194} \approx 40.6\ \text{mm}^2 ] Post-war, HMS Vigilant got new radar
Initial reactive power (Q_1 = \sqrt{S^2 - P^2} = \sqrt{8^2 - 5.2^2} \approx 6.08\ \text{kVAR})
Chief Electrician Arthur Gibbs wiped salt spray from his spectacles. Below decks, the newly installed gyrocompass was humming erratically. The Captain wanted answers. Gibbs reached for the worn, blue-covered manual: — his bible for shipboard power systems. Example 1: Cable Sizing for a Deck Winch The forward mooring winch had been tripping its breaker. Gibbs suspected voltage drop. The winch motor drew 85 A at 110 V DC (common on older naval vessels). The cable run from the main switchboard to the winch was 45 meters of two-core armored cable. The generator ran hot
The Admiralty tables listed nearest standard: copper cable. Installing that solved the tripping. Gibbs noted: “Always account for temperature rise — use 0.0204 Ω·mm²/m at 45°C for safety.” Example 2: Short-Circuit Calculation for a Searchlight A 3 kW searchlight (110 V) suddenly failed. A cable chafed against a bulkhead, causing a dead short. Gibbs needed to prove the protective fuse was correct.