brake vs indicated Mean effective pressure

 Brake Mean Effective Pressure (BMEP) vs. Indicated Mean Effective Pressure (IMEP)

Both BMEP and IMEP are key parameters in engine performance analysis, representing average pressure acting on the piston during power generation. However, they differ in what they measure:

---

1. Indicated Mean Effective Pressure (IMEP)

Definition:
The average pressure that, if applied uniformly over the piston’s stroke, would produce the indicated power (IP) of the engine.

Formula:

$$����=\frac{��\times 60}{�\cdot �\cdot �\cdot �}$$

Where:

• $��$ = Indicated Power (W or kW)

• $�$ = Stroke length (m)

• $�$ = Piston area ($�{�}^2\mathrm{/}4$) (m²)

• $�$ = Engine speed (RPM)

• $�$ = Number of power strokes per revolution

  • For a 4-stroke engine, $�=�\mathrm{/}2$ (since power is generated every 2 revolutions).

  • For a 2-stroke engine, $�=�$.

Key Points:

• Represents theoretical cylinder pressure before mechanical losses.

• Measured from an indicator diagram (P-V curve).

• Higher than BMEP because it doesn’t account for friction.

---

2. Brake Mean Effective Pressure (BMEP)

Definition:
The average pressure that would produce the brake power (BP) if applied uniformly over the piston stroke.

Formula:

$$����=\frac{��\times 60}{�\cdot �\cdot �\cdot �}$$

(Where variables are the same as in IMEP, but using BP instead of IP.)

Alternative Formula (Using Torque):
For a 4-stroke engine:

$$����=\frac{2�\cdot �\cdot {�}_{�}}{{�}_{�}}$$

Where:

• $�$ = Torque (Nm)

• ${�}_{�}$ = Number of crankshaft revolutions per power stroke (2 for 4-stroke, 1 for 2-stroke)

• ${�}_{�}$ = Displacement volume ($�\cdot �\cdot {�}_{���}$)

Key Points:

• Represents actual usable pressure after friction losses.

• Used to compare engines of different sizes (higher BMEP = more efficient engine).

• Typical values:

  • Naturally aspirated petrol engine: 8–12 bar

  • Turbocharged diesel engine: 15–25 bar

---

3. Relationship Between IMEP, BMEP, and FMEP

$$����=����-����$$

Where:

• FMEP (Friction Mean Effective Pressure) = Average pressure lost due to friction.

Mechanical Efficiency (η) can also be expressed as:

$$�=\frac{����}{����}\times 100\mathrm{\%}$$

---

Summary Table

Parameter	Definition	Depends On	Typical Use
IMEP	Avg. pressure for indicated power	Combustion efficiency, cylinder pressure	Engine design analysis
BMEP	Avg. pressure for brake power	Torque, engine load	Performance benchmarking
FMEP	Avg. pressure lost to friction	Engine design, lubrication	Efficiency improvement

---

Example Calculation

Given:

• 4-stroke engine, 1 cylinder

• Bore = 80 mm, Stroke = 90 mm

• Speed = 3000 RPM

• Indicated Power (IP) = 25 kW

• Brake Power (BP) = 20 kW

Step 1: Calculate Piston Area (A)

$$�=\frac{�{�}^2}{4}=\frac{�(0.08{)}^2}{4}=0.005026\text{m²}$$

Step 2: Calculate IMEP

$$����=\frac{��\times 60}{�\cdot �\cdot �\cdot �}=\frac{25000\times 60}{0.09\times 0.005026\times 3000\times (3000\mathrm{/}2)}$$

(For 4-stroke, $�=�\mathrm{/}2$)

$$����\approx 7.38\text{bar}$$

Step 3: Calculate BMEP

$$����=\frac{��\times 60}{�\cdot �\cdot �\cdot �}=\frac{20000\times 60}{0.09\times 0.005026\times 3000\times 1500}$$$$����\approx 5.90\text{bar}$$

Step 4: Calculate FMEP

$$����=����-����=7.38-5.90=1.48\text{bar}$$

Step 5: Mechanical Efficiency

$$�=\frac{����}{����}\times 100\mathrm{\%}=\frac{5.90}{7.38}\times 100\mathrm{\%}\approx 80\mathrm{\%}$$

---

Key Takeaways

• IMEP = Theoretical max pressure (from combustion).

• BMEP = Actual usable pressure (after friction).

• Higher BMEP = More efficient engine.

• FMEP = Losses due to friction (can be reduced by better lubrication, lighter components)