Engine performance testing and heat balance

Why it matters

Every engine claim, from rated power to fuel economy to emission certification, rests on a test-bed measurement. Performance testing tells you how much of the fuel energy reaches the crankshaft, where the rest goes, and how friction, load and speed change the picture. University practicals, GATE numericals and engine-development jobs all use the same small set of definitions, so they are worth knowing precisely.

Key ideas

Measured quantities on a test bed

• Speed N (tachometer or encoder) and torque T (dynamometer: hydraulic, eddy-current, or electrical; small labs use a rope brake). Brake power is computed from these two, never measured directly.
• Fuel flow (burette and stopwatch, gravimetric balance or Coriolis meter).
• Air flow (orifice meter with an air box to damp pulsations, or a hot-film sensor).
• Cylinder pressure against crank angle (piezoelectric transducer), integrated to give indicated work.
• Coolant flow and inlet/outlet temperatures; exhaust temperature and composition; ambient pressure, temperature and humidity (used to correct power to standard conditions).

Power terms

• Indicated power (IP): power developed by the gas on the pistons, from the area of the measured p–V (indicator) diagram. It is a measured quantity, not a theoretical one.
• Brake power (BP): power available at the crankshaft, from torque and speed.
• Friction power (FP = IP − BP): rubbing friction, pumping work of the gas exchange (in the brake-based definition), and accessory drives. FP rises with speed and with oil viscosity; at part load it is a larger fraction of IP, so mechanical efficiency falls as load falls.

Finding friction power when no indicator is available

• Willans line (CI engines): plot fuel flow against BP at constant speed and extrapolate the nearly straight line back to zero fuel; the negative BP intercept is FP. Not used for SI engines because the throttled fuel line is not straight.
• Morse test (multi-cylinder SI engines): at constant speed, cut each cylinder in turn and re-adjust the dynamometer to restore speed. The drop in BP equals the indicated power of the cut cylinder (its friction is unchanged).
• Motoring test: drive the engine with an electric dynamometer at the same speed and temperature; the motoring power approximates FP. It is only an estimate, because cylinder pressures, ring loading and gas temperatures are not the same as in a firing engine.
• Retardation test: time the speed fall after cutting fuel.

Efficiencies and specific quantities

• Brake thermal efficiency, indicated thermal efficiency and mechanical efficiency (η_bth = η_m × η_ith).
• Volumetric efficiency compares the air actually inducted with the air that would fill the swept volume at intake (or ambient) density.
• Brake specific fuel consumption (bsfc) is the cleanest comparison of fuel economy; typical full-load values are about 0.20–0.25 kg/kWh for automotive diesels and 0.25–0.30 kg/kWh for petrol engines.
• Mean effective pressure (mep) is the constant pressure that, acting over one stroke per power cycle, gives the same work; brake mep normalises torque for size, so it compares engines of different capacity.

Heat balance sheet: at a steady operating point the fuel energy rate is split into brake power, heat to coolant, heat in the exhaust (sensible enthalpy above ambient), and an unaccounted remainder (radiation, convection from the block, heat to oil, incomplete combustion, measurement error). Typical full-load shares: brake 25–40%, coolant 20–35%, exhaust 25–40%, unaccounted 5–10%. A heat balance shows where recovery (turbocharging, exhaust heat recovery) is worth pursuing.

Performance curves: at full throttle, torque peaks at mid speed (best volumetric efficiency), power peaks at higher speed, and bsfc has a minimum near the torque peak. Constant-speed tests at varying load show η_m and η_bth rising with load.

Formulas

BP = 2π · N · T / 60

• BP: brake power (W); N: speed (rpm); T: torque (N·m).

IP = pmi · L · A · n · k

• pmi: indicated mean effective pressure (Pa); L: stroke (m); A: piston area (m²); n: power strokes per second per cylinder (N/120 for four-stroke, N/60 for two-stroke); k: number of cylinders.

FP = IP − BP, η_m = BP / IP

η_bth = BP / (ṁ_f · CV), η_ith = IP / (ṁ_f · CV)

• ṁ_f: fuel mass flow (kg/s); CV: lower calorific value (J/kg).

bsfc = ṁ_f / BP

• Usually quoted in kg/kWh: bsfc = 3600 · ṁ_f[kg/s] / BP[kW].

bmep = BP · n_R / (V_s · N/60)

• bmep: brake mean effective pressure (Pa); V_s: total swept volume (m³); n_R = 2 for four-stroke, 1 for two-stroke.

η_v = ṁ_a / (ρ_a · V_s · N / (60 · n_R))

• ṁ_a: actual air flow (kg/s); ρ_a: air density at intake conditions (kg/m³).

Q̇_cw = ṁ_w · c_pw · (T_out − T_in) and Q̇_ex = ṁ_g · c_pg · (T_ex − T_amb)

• Heat to coolant and to exhaust (W); ṁ_g = ṁ_a + ṁ_f (kg/s).

Worked examples

Example 1 (standard): performance and heat balance of a diesel engine. Given: four-stroke, four-cylinder diesel, V_s = 2.2 L, at 2,400 rpm the dynamometer reads T = 150 N·m. Fuel 9.6 kg/h, CV = 42,500 kJ/kg. FP (Willans line) = 8 kW. Coolant 0.7 kg/s, rise 13 K, c_pw = 4.18 kJ/kg·K. Exhaust 0.055 kg/s at 750 K, ambient 300 K, c_pg = 1.1 kJ/kg·K.

1. BP = 2πNT/60 = 2π × 2400 × 150/60 = 37,699 W = 37.70 kW.
2. Fuel energy: ṁ_f · CV = (9.6/3600) × 42,500 = 113.33 kW.
3. η_bth = 37.70/113.33 = 33.3%. bsfc = 9.6/37.70 = 0.255 kg/kWh.
4. IP = BP + FP = 45.70 kW; η_m = 37.70/45.70 = 82.5%; η_ith = 45.70/113.33 = 40.3%.
5. bmep = BP · 2/(V_s · N/60) = 37,699 × 2 / (0.0022 × 40) = 8.57 × 10⁵ Pa = 8.57 bar.
6. Coolant: 0.7 × 4.18 × 13 = 38.04 kW (33.6%). Exhaust: 0.055 × 1.1 × 450 = 27.23 kW (24.0%). Unaccounted: 113.33 − 37.70 − 38.04 − 27.23 = 10.37 kW (9.2%). Answer: BP = 37.7 kW, η_bth = 33.3%, bsfc = 0.255 kg/kWh, bmep = 8.57 bar; heat balance 33.3% brake, 33.6% coolant, 24.0% exhaust, 9.2% unaccounted.

Example 2 (GATE level): Morse test. Given: four-cylinder SI engine at constant speed, BP with all cylinders firing = 30 kW. BP with cylinders 1, 2, 3, 4 cut in turn = 21.0, 21.2, 20.8, 21.0 kW.

1. Indicated power of each cylinder: IP_i = BP_all − BP_(i cut) = 9.0, 8.8, 9.2, 9.0 kW.
2. IP = ΣIP_i = 36.0 kW.
3. FP = IP − BP = 36.0 − 30.0 = 6.0 kW.
4. η_m = BP/IP = 30/36 = 0.833. Answer: IP = 36.0 kW, FP = 6.0 kW, η_m = 83.3%.

Common mistakes

• Forgetting the factor 2 (n_R) for four-stroke engines in IP and bmep.
• Using rpm directly as rad/s; BP = T·ω with ω = 2πN/60.
• Mixing kg/h with kg/s or kJ with kW·h in bsfc; 1 kWh = 3,600 kJ.
• Using the higher calorific value when the data book or question specifies the lower one.
• Taking exhaust heat as ṁ_a·c_p·T_ex instead of the rise above ambient, and leaving out the fuel mass.
• Applying the Willans line to a throttled SI engine.
• Quoting a brake thermal efficiency above about 45–50%: for an automotive engine that signals an arithmetic or unit error.

For GATE ME

Questions are almost always numerical: BP from torque and speed, IP from imep and geometry, mechanical and thermal efficiencies, bsfc, bmep, volumetric efficiency, Morse-test and Willans-line friction power, and the shares in a heat balance. Practise unit conversions between kg/h, kg/s, kW and kWh, and remember the four-stroke factor.

Quick check

1. Torque 100 N·m at 3,000 rpm. Brake power?
2. IP = 50 kW, FP = 10 kW. Mechanical efficiency?
3. Why is a Morse test not possible on a single-cylinder engine?
4. Fuel 6 kg/h for 24 kW brake power. bsfc?

Answers: 1. 31.4 kW. 2. 80%. 3. Cutting the only cylinder stops the engine, so there is no running reference. 4. 0.25 kg/kWh.