⚡ THE MOST IMPORTANT FORMULAS FOR A SHIP’S ETO
A good ETO doesn’t calculate everything from memory.
But he knows which formula to use — and what the result should roughly look like.
Here is the essential electrical cheat sheet 👇
🔹 1. OHM’S LAW
I = V / R
V = I × R
R = V / I
The starting point for most electrical troubleshooting.
🔹 2. DC POWER
P = V × I
For a 24 V DC circuit drawing 10 A:
P = 240 W
🔹 3. THREE-PHASE POWER
P = √3 × V × I × cosφ
This is one of the most important formulas on a ship.
Use it for generators, motors and large AC consumers.
🔹 4. APPARENT POWER
S = √3 × V × I
S is measured in kVA.
And:
cosφ = P / S
🔹 5. REACTIVE POWER
Q = √(S² − P²)
Measured in kVAr.
🔹 6. POWER FACTOR
cosφ = kW / kVA
Low power factor = higher current for the same useful power.
Higher current = more losses and voltage drop.
🔹 7. RESISTANCE
R = ρL / A
Resistance increases with:
• longer conductor
• higher resistivity
• smaller cross-section
🔹 8. THREE-PHASE CURRENT
I = P / (√3 × V × cosφ)
Very useful when estimating motor or load current.
🔹 9. MOTOR SYNCHRONOUS SPEED
nₛ = 120f / P
Where:
f = frequency, Hz
P = number of poles
At 50 Hz:
2-pole → 3000 rpm
4-pole → 1500 rpm
6-pole → 1000 rpm
🔹 10. MOTOR SLIP
s = (nₛ − n) / nₛ × 100%
Example:
1500 rpm synchronous speed
1450 rpm actual speed
Slip ≈ 3.3%
🔹 11. TRANSFORMER RATIO
V₁ / V₂ = N₁ / N₂
More turns → higher voltage.
Fewer turns → lower voltage.
🔹 12. TRANSFORMER CURRENT
V₁I₁ ≈ V₂I₂
For an ideal transformer.
Voltage goes down → current goes up.
🔹 13. ELECTRICAL ENERGY
E = P × t
If a 10 kW heater operates for 5 hours:
E = 50 kWh
🔹 14. CAPACITIVE REACTANCE
Xc = 1 / (2πfC)
Frequency increases → capacitive reactance decreases.
🔹 15. INDUCTIVE REACTANCE
Xl = 2πfL
Frequency increases → inductive reactance increases.
🔹 16. TOTAL SERIES RESISTANCE
Rₜ = R₁ + R₂ + R₃ + …
🔹 17. PARALLEL RESISTANCE
1/Rₜ = 1/R₁ + 1/R₂ + 1/R₃ + …
For two resistors:
Rₜ = R₁R₂ / (R₁ + R₂)
🔹 18. BATTERY ENERGY
E ≈ V × Ah
Example:
24 V × 200 Ah ≈ 4.8 kWh
Real available energy will be lower due to losses and discharge conditions.
🔹 19. VOLTAGE DROP
ΔV = I × R
The longer the cable and the higher the current, the greater the voltage drop.
🔹 20. EFFICIENCY
η = Pout / Pin × 100%
A motor taking 100 kW and delivering 90 kW mechanically:
η = 90%
⚠️ ETO GOLDEN RULE
A formula gives you a number.
Troubleshooting gives you the reason.
If the measured value doesn’t make sense, don’t blame the formula first.
Check:
Voltage → Current → Resistance → Load → Connections → Protection
⚓ RhumbFleet
Professional Maritime Knowledge. Real Experience. Continuous Learning.
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