1.3 Compression Ratio, Manifold Pressure & Power Calculations

1.3 Compression Ratio, Manifold Pressure & Power Calculations

Quick Answer: Engine power output is governed by cylinder displacement geometry, compression ratio, induction pressure, and thermodynamic efficiency. The PLANK formula ($PLANK / 33,000$) calculates Indicated Horsepower (IHP), the total chemical-thermal power generated in the cylinders. Brake Horsepower (BHP) is the actual usable shaft power delivered to the propeller after subtracting Friction Horsepower (FHP). Manifold Absolute Pressure (MAP) directly measures induction charge density. Independent FAA AMT Powerplant prep by OpenExamPrep.

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Compression Ratio (CR) Geometry and Mechanics

Compression ratio is a volumetric ratio that compares the maximum internal volume of a cylinder when the piston is at Bottom Dead Center (BDC) to the minimum volume remaining when the piston reaches Top Dead Center (TDC):

$\text{Compression Ratio (CR)} = \frac{V_{\text{total}}}{V_c} = \frac{V_d + V_c}{V_c}$

Where:

• $V_d$ = Piston Displacement: The physical volume swept out by the piston crown as it travels the length of its stroke from TDC to BDC.
• $V_c$ = Clearance Volume: The volume remaining inside the combustion chamber above the piston crown when the piston is at the very top of its stroke (TDC).

  +------------------------+  <-- Cylinder Head
  |  Clearance Volume (Vc) |  <-- Piston at TDC
  +========================+  
  |                        |  ^
  |                        |  |
  |                        |  | Stroke (L)
  |   Piston Displacement  |  | Piston sweeps Vd
  |          (Vd)          |  |
  |                        |  v
  +========================+  <-- Piston at BDC
  |      Crankcase         |

Piston Displacement Formula

The piston displacement of a single cylinder is calculated from its bore (internal cylinder diameter, $B$) and its stroke (piston travel distance, $S$ or $L$):

$V_d = \frac{\pi \times B^2 \times S}{4} = \pi \times r^2 \times S$

To find the total engine displacement, multiply single-cylinder displacement ($V_d$) by the total number of cylinders ($K$): $\text{Total Engine Displacement} = V_d \times K$

Worked Example: An aircraft engine has a 5.125-inch cylinder bore, a 4.375-inch stroke, and a clearance volume ($V_c$) of 11.28 cubic inches. Find its compression ratio:

1. $V_d = \frac{\pi \times (5.125)^2 \times 4.375}{4} = 0.7854 \times 26.2656 \times 4.375 \approx 90.25\text{ cu in}$.
2. $V_{\text{total}} = V_d + V_c = 90.25 + 11.28 = 101.53\text{ cu in}$.
3. $\text{CR} = \frac{101.53}{11.28} \approx 9.0:1$.

Thermodynamic Significance of Compression Ratio

Increasing the compression ratio directly increases the engine's thermal efficiency and reduces Specific Fuel Consumption (SFC). Compressing the fuel-air charge more tightly forces fuel molecules closer to oxygen, increases mixture temperature prior to ignition, accelerates combustion velocity, and allows expanding gases to extract more mechanical work across a longer effective expansion ratio.

However, compression ratio is physically limited by the anti-knock (detonation) rating of aviation gasoline. Exceeding design compression ratios causes the compressed mixture to reach its auto-ignition temperature, producing catastrophic detonation. Modern high-compression aircraft engines (e.g., 8.5:1 or 8.7:1) mandate 100LL avgas, whereas low-compression engines (e.g., 7.0:1) can safely operate on lower-octane fuels or approved unleaded aviation gasolines.

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Manifold Absolute Pressure (MAP) Dynamics

The Manifold Absolute Pressure (MAP) gauge is an absolute pressure-sensing flight instrument connected to the engine induction intake runner downstream of the throttle plate. It measures the absolute pressure of the fuel-air charge delivered to the cylinders in inches of mercury (inHg).

The Static MAP Gauge Principle

A fundamental question on the FAA Powerplant examination tests candidate understanding of a stopped engine: When an aircraft engine is not running, what does the manifold pressure gauge indicate? Because the manifold gauge contains an evacuated aneroid bellows that references absolute zero pressure, it registers the prevailing atmospheric barometric pressure of the surrounding airfield. At sea level on a standard day (ISA standard), it indicates 29.92 inHg. At an airport located at 5,000 feet elevation, it indicates approximately 24.9 inHg.

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Power Hierarchy: Indicated, Brake, and Friction Horsepower

Power is defined as the rate of doing work. In English engineering units, one horsepower (hp) equals 33,000 foot-pounds of work per minute (or 550 foot-pounds per second), a standard established by James Watt.

[ Total Chemical Energy in Fuel ]
               |
               v
[ Indicated Horsepower (IHP) ] <--- Total power generated in cylinders
       |               |
       | (Losses)      v
       |          [ Friction Horsepower (FHP) ] <--- Internal friction & accessories
       v
[ Brake Horsepower (BHP) ] <--- Usable shaft power delivered to propeller

1. Indicated Horsepower (IHP)

Indicated Horsepower is the total theoretical power developed by the expanding combustion gases inside the engine cylinders, completely ignoring all internal mechanical friction and pumping losses. It is calculated directly from cylinder pressure data using the PLANK formula.

2. Brake Horsepower (BHP)

Brake Horsepower is the actual, net usable mechanical power delivered by the engine crankshaft to the propeller shaft. It is termed "brake" horsepower because it was historically measured by applying a mechanical friction brake (prony brake) or dynamometer to the output shaft:

$\text{BHP} = \frac{2\pi \times \text{Torque (ft-lb)} \times \text{RPM}}{33,000} = \frac{\text{Torque} \times \text{RPM}}{5,252}$

3. Friction Horsepower (FHP)

Friction Horsepower is the power consumed by the engine in turning itself over. It represents the difference between theoretical power developed and net power delivered:

$\text{FHP} = \text{IHP} - \text{BHP}$

Friction horsepower losses stem from three primary sources:

1. Mechanical Sliding Friction: Piston rings sliding against cylinder walls (accounts for over 50% of total FHP), crankshaft main and rod journals rotating in sleeve bearings, and rocker arm bushings.
2. Pumping Losses: Work consumed during the intake and exhaust strokes in drawing in fresh charge and pushing spent exhaust gases through restricted ports and manifolds.
3. Accessory Drive Consumption: Power consumed driving engine-mounted accessories, including dual magnetos, the engine oil pump, scavenge pumps, fuel injection pumps, alternator, and internal supercharger impellers.

4. Mechanical Efficiency ($\eta_m$)

Mechanical efficiency is the ratio of usable shaft power delivered to total power developed:

$\eta_m = \frac{\text{BHP}}{\text{IHP}} \times 100\%$

In well-engineered, modern aircraft reciprocating engines operating at rated power, mechanical efficiency typically ranges between 85% and 90%.

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The PLANK Formula for Indicated Horsepower

The most famous equation on the FAA Aviation Maintenance Technician examination is the PLANK formula, used to compute Indicated Horsepower:

$\text{IHP} = \frac{P \cdot L \cdot A \cdot N \cdot K}{33,000}$

Every parameter in this equation has a rigorous engineering definition and specific unit requirements:

CRITICAL EXAM WARNING ($N$ Trap): On the FAA exam, candidate failure on PLANK questions almost always stems from using full engine RPM for $N$. In a four-stroke engine, a cylinder produces a power stroke only once every two revolutions. Therefore, $N$ must always equal $\text{RPM} / 2$.

Comprehensive PLANK Step-by-Step Calculation

Problem: Calculate the Indicated Horsepower of a six-cylinder ($K = 6$) four-stroke aircraft engine operating at 2,400 RPM with an Indicated Mean Effective Pressure ($P$) of 140 psi, a cylinder bore of 5.0 inches, and a stroke of 4.5 inches.

1. Determine Stroke in Feet ($L$): $L = \frac{4.5\text{ in}}{12} = 0.375\text{ ft}$
2. Determine Piston Area ($A$): $A = \frac{\pi \times (5.0)^2}{4} = 0.7854 \times 25.0 = 19.635\text{ sq in}$
3. Determine Power Strokes per Minute per Cylinder ($N$): $N = \frac{2,400\text{ RPM}}{2} = 1,200\text{ power strokes/min}$
4. Apply the PLANK Formula: $\text{IHP} = \frac{140 \times 0.375 \times 19.635 \times 1,200 \times 6}{33,000}$ $\text{Numerator} = 140 \times 0.375 \times 19.635 \times 1,200 \times 6 = 7,422,030\text{ ft-lb/min}$ $\text{IHP} = \frac{7,422,030}{33,000} \approx 224.9\text{ IHP}$

If this engine exhibits a mechanical efficiency of 88%, its usable Brake Horsepower is: $\text{BHP} = \text{IHP} \times \eta_m = 224.9 \times 0.88 = 197.9\text{ BHP}$ Friction horsepower consumed internally is: $\text{FHP} = \text{IHP} - \text{BHP} = 224.9 - 197.9 = 27.0\text{ FHP}$

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Efficiencies: Thermal, Volumetric, and BSFC

• Brake Specific Fuel Consumption (BSFC): The mass of fuel consumed per hour per unit of brake horsepower produced: $\text{BSFC} = \text{Fuel Flow (lb/hr)} / \text{BHP}$. Typical aviation reciprocating values range between 0.42 and 0.48 lb/(BHP·hr) at cruise.
• Thermal Efficiency ($\eta_{th}$): The percentage of total chemical energy in the consumed fuel converted into mechanical shaft work. Aircraft reciprocating engines achieve 30% to 34% thermal efficiency; the remaining 66% to 70% is rejected as waste heat to exhaust gas (~45%), cylinder cooling fins (~15%–20%), and engine lubricating oil (~5%–10%).
• Volumetric Efficiency ($\eta_v$): The ratio of the mass of fuel-air charge inducted into the cylinder to the theoretical mass that would completely fill the cylinder displacement volume under static ambient conditions. Sharp induction bends, high carburetor heat, and restrictive air filters reduce volumetric efficiency.