Estimating Piston Engine Power Output

(Created September 2009)
(Revised and Clarified August 2016)

Basic Equation for Piston Engine Power Output

P = (n * ( π / 4 ) * D2 * L) * p * N

Equation Explained

Example

We have an 8-cylinder four-stroke diesel engine at 2000 RPM, with a bore of 115mm, a stroke of 135mm and a BMEP of 10 bar. What is the power output of the engine in mechanical horsepower?

First, we have to convert everything to a form useable by the equation.

2000 RPM / 60 = 33 RPS / 2 = 16 firing strokes per second – THIS ONE IS REALLY IMPORTANT! IF YOU TRY TO ENTER RPM DIVIDED BY TWO, THE ANSWER WILL BE TOTALLY WRONG. YOU MUST CONVERT TO FIRING STROKES PER SECOND!

115mm Piston Diameter * 0.001 = 0.115 m piston diameter

135mm Piston Stroke * 0.001 = 0.135 m piston stroke

10 bar BMEP * 100,000 = 1,000,000 N/m2

P = (8 * ( π / 4 ) * 0.1152 * 0.135) * 1,000,000 * 16

P = 179485.4715 Watts * 0.00134102 = 240.693 mechanical horsepower

Thus, the engine mentioned above would have an output of about 240.7 hp at the given inputs.

Conversion Table (for when you don't have access to the internet):

1 Bar = 100,000 N/m2
1 Watt = 0.00134102 mechanical horsepower
1 millimeter = 0.001 meter

Reference:
Technology of Tanks by R.M. Ogorkiewicz

Equation for Estimating Brake Mean Effective Pressure

BMEP = ( ( π / 4 ) T ) / D

Where:

BMEP = Brake Mean Effective Pressure (N/m2).
T = Torque (Nm).
D = Displacement (m3).

Example

We have a 23 liter engine that produces 1,660 Nm of torque. What is it's BMEP?

23 Liters * 0.001 = 0.023 m3.

( ( π / 4 ) 1,660 ) / 0.023 = 906,964.14 N/m2

906,964.14 N/m2 / 100,000 = 9.0696 Bar

Conversion Table (for when you don't have access to the internet):

1 Liter = 0.001 m3
1 Bar = 100,000 N/m2

Reference:
Wikipedia on Mean Effective Pressure (LINK)

Equation for Estimating Piston Speed

MPS = ( 2 * Stroke * RPM ) / 60

Where:

MPS = Mean Piston Speed (m/sec)
Stroke = Piston Stroke Length (meters)
RPM = Revolutions per Minute

Example:

You have an engine with a stroke length of 175mm and a RPM of 2,500. What is it's mean piston speed?

175mm = 0.175 meters

MPS = ( 2 * 0.175 * 2500 ) / 60 = 14.583 m/sec

The estimated piston speed is 14.583 m/sec.

Calculating Engine Displacement

D = [ (π * (B/2)2 * S ) * C ] * 0.000001

Where:

D = Displacement (Liters)
B = Piston Bore (mm)
S = Piston Stroke (mm)
C = Number of Cylinders

Example:

Our engine has 8 cylinders, a bore of 100mm and a stroke of 78mm. What is it's displacement?

D = [ (π * (100/2)2 * 78 ) * 8 ] * 0.000001 = 4.90088454 Liters

Estimating Engine Weights

To estimate engine weights is somewhat complicated; due to the fact that the more cylinders a engine has, the more efficient it's horsepower to weight ratio is.

This is due to the fact that there's a large fixed cost for engine accessories (Magnetos, carburetors, etc), but as you add more cylinders, the cost of adding a slightly larger Magneto to support the additional cylinders is marginal compared to the original installation cost.

To take this into account, the “Adjusted Specific Weight” formula was developed, based off the MTU MB 870 Generation 1 family specifications (as it was a whole family from 6 to 12 cylinders, providing many data points).

Adjusted Specific Weight = BSW + ( -2.14 * C)

Where:

BSW = Basic Specific Weight (kg/L)
C = Number of Cylinders the engine has

Example:

Our engine has 12 cylinders and has a Basic Specific Weight of 50 kg/L. What is it's Adjusted Specific Weight?

Adjusted Specific Weight = 50 + ( -2.14 * 12) = 24.32 kg/L

You can now calculate the estimated weight of the engine:

Weight = Displacement * Adjusted Specific Weight

Thus, a 6.7 liter engine with a ASW of 24.32 kg/L would be:

6.7 * 24.32 = 162.9 kg.

Engine Specifications

Naturally Aspirated Gasoline Engines

Year: 1940s Tank Engines
BMEP: 7.5 to 9.85 bar (HL120 to Ford GAA); average of 8.675 bar
BSW: 102.7 to 54.1 kg/L (HL120 to Ford GAA); average of 78.4 kg/L

Notes: An idea of the difference that raw materials make is the HL210 having a BSW of 65.5 kg/L due to having an aluminum engine block, while the later HL230 (which was essentially the same as the HL210 but with bored out cylinders) had a BSW of 77.65 kg/L due to cast iron replacing aluminum in the construction of the motor.

Lightly Turbocharged Gasoline Engines

Year: 1962 (Oldsmobile Jetfire) and 1975 (Porsche 930 Turbo Carrera)
BMEP: 12~ bar (Oldsmobile) to 13.58 (Porsche 930 Turbo)
BSW: 60.8 kg/L

Notes: The Jetfire was based upon the Buick “Small Block” 215 aluminum V8, which was for a time, the lightest mass production V8 in the world.

Moderately Turbocharged Gasoline Engines

Year: 1987 (Ferrari F40 Supercar)
BMEP: 20.95~ bar
BSW: Unknown kg/L

Deeply Turbocharged Gasoline Engines

Year: 2013 (Koenigsegg Agera S)
BMEP: 27~ bar
BSW: 56.32 kg/L

Notes: The Koenigsegg' engine's light weight is due to an aluminum block and carbon fiber intake manifold.

Naturally Aspirated Diesels

Year: 1940s – 1950s Tank Engines
BMEP: 6 to 6.4 ~ bar
BSW: 38.3 to 48.8 kg/L

Notes: Examples of these include the T-34's V-2-34 diesel, and the various diesels put forth by the US during WW2.

Lightly Turbocharged Diesels

Year: 1960s Tank Engines (MTU 838)
BMEP: 9.15~ bar
BSW: 67.5~ kg/L

Notes: Development on these began in the mid to late 1940s, and they entered service in the late 1950s and early 1960s.

Moderately Turbocharged Diesels

Year: 1970s Tank Engines / 1990s Road Diesels: (MTU 873 and 7.3L PS)
BMEP: 11 to 13.4~ bar
BSW: 74.5 to 80~ kg/L

Notes: Development on these began in 1965 by MTU, with them being available for military purposes in the 1970s. Initially, they were produced with 13~ bar BMEP (original MTU 873 prototype), but the turbocharger technology wasn't up to it at the time (severe turbo lag), so they were reduced down to 11~ bar to improve torque and acceleration characteristics.

Deeply Turbocharged Diesels

Year: 2000s Tank Engines / 2010s Road Diesels: (MTU 883 and 6.7L PS)
BMEP: 20~ bar
BSW: 87~ kg/L

Notes: Development on these began in 1970 by MTU, with them being available for military purposes in the 1990s. When they were first installed in tanks (Merkava Mk 3 in the 2000s) and in pickup trucks (Ford's 6.0L Powerstroke had a BMEP of 15~), there were significant problems with them grenading in both applications.

Extremely (Hyperbar) Turbocharged Diesels

Year: 1990s Tank Engines (V8X on LeClerc)
BMEP: 30 to 33.9~ bar
BSW: 144~ kg/L

Notes: This concept uses a separate gas turbine engine to act as a supercharger for the diesel engine (and to act as an APU when the diesel engine is shut down. It was first invented in the late 1970s with bench engines in the 1980s, and it's only application (so far as of 2016) is in the LeClerc's engine.