Vigilada Mineducación

Propulsión I
MSc. Juliana Andrea Niño Navia
La siguiente presentación ha sido realizada con base en información obtenida de diversos manuales de fabricante así como de
libros referenciados al inicio del curso. Las imágenes fueron obtenidas en la red y ninguna de ellas tiene derechos reservados de
autor.

Sin Límites 1
 TORQUE AND POWER

Torque is a good indicator of a engine´s ability to do work. It is

defined as force acting a moment distance. Torque τ is related to
work by:
𝑉𝑉𝑑𝑑
2𝜋𝜋𝜋𝜋 = 𝑊𝑊𝑏𝑏 = 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 (34)
𝑛𝑛

Where: 𝑊𝑊𝑏𝑏 = brake work of one revolution;

𝑉𝑉𝑑𝑑 = displacement volume;
n = number of revolutions per cycle.

For a two stroke cycle engine with one cycle for each revolution:

Vigilada Mineducación
2𝜋𝜋𝜋𝜋 = 𝑊𝑊𝑏𝑏 = 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑉𝑉𝑑𝑑 (35)

Sin Límites
 TORQUE AND POWER
𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑉𝑉𝑑𝑑
𝜏𝜏 = (36)
2𝜋𝜋

For a four stroke cycle engine with one cycle for each revolution:
𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑉𝑉𝑑𝑑
𝜏𝜏 = (37)
4𝜋𝜋

In these equations, bmep and brake work 𝑊𝑊𝑏𝑏 are used because
torque is measured off the output crankshaft.

Many modern automobile engines have maximum torque in the

Vigilada Mineducación
200 to 300 N.m range at engine speeds are usually around 4000 to
6000 rpm. The point of maximum torque is called maximum brake
torque speed (MBT) .

Sin Límites
 TORQUE AND POWER

CI engines generally have greater torque than SI engines. Large

engines often have very high torque values with MBT at relatively
low speed.

Vigilada Mineducación
Sin Límites Source:
Internal Combustion Engine Fundamentals –J. B.
Heywood. McGraw-Hill 1988, 1st Edition, USA, NJ
 TORQUE AND POWER

Power is defined as the rate of work of the engine. If n= number of

revolutions per cycle and N = engine speed, then:

𝑊𝑊𝑊𝑊
𝑊𝑊̇ = (38)
𝑛𝑛

𝑊𝑊̇𝑏𝑏 = 2𝜋𝜋𝜋𝜋𝜋𝜋 (39)

1
𝑊𝑊̇ = � 𝑚𝑚𝑚𝑚𝑚𝑚 � 𝐴𝐴𝑝𝑝 � 𝑆𝑆𝑝𝑝 (40)
2𝑛𝑛

𝐴𝐴𝑝𝑝 � 𝑆𝑆𝑝𝑝
𝑊𝑊̇ = 𝑚𝑚𝑚𝑚𝑚𝑚 � Four Stroke Cycle (41)

Vigilada Mineducación
4

𝐴𝐴𝑝𝑝 � 𝑆𝑆𝑝𝑝
𝑊𝑊̇ = 𝑚𝑚𝑚𝑚𝑚𝑚 � Two Stroke Cycle (42)
2

Sin Límites
 TORQUE AND POWER

Depending upon which definition of work or mep is used in the eq

38- 42, power can be defined as brake power, net indicated power,
gross indicated power, pumping indicated power, and even friction
power, also:
𝑊𝑊̇𝑏𝑏 = η𝑚𝑚 𝑊𝑊̇ 𝑖𝑖 (43)

𝑊𝑊̇ 𝑛𝑛𝑛𝑛𝑛𝑛 = 𝑊𝑊̇ 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 − 𝑊𝑊̇ 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 (44)

𝑊𝑊̇𝑏𝑏 = 𝑊𝑊̇ 𝑖𝑖 − 𝑊𝑊𝑓𝑓̇ (45)

Vigilada Mineducación
Where η𝑚𝑚 is the mechanical efficiency of the engine

Sin Límites
 TORQUE AND POWER

Engine power can range from a few watts in small model airplanes engines
to thousands of kW per cylinder in large multiple – cylinder stationary and
ship.

Power for outboard motors (engines) for small boats typically ranges from
2 to 40 kW ( 3-50 hp), with much larger ones available. Modern automobile
engines range mostly from 40 to 220 kW.

Both torque and power are functions of engine speed. At low speed, torque
increases as engine speed increased. As engine speed increases further,
torque reach maximum and then decreases. Torque decreases because the
engine is unable to ingest full charge of air at higher speeds.

Vigilada Mineducación
Indicated power increases with speed, while brake power increases to a
maximum and then decreases at higher speeds.

Sin Límites
 TORQUE AND POWER
Other ways which are sometimes used to classify engines are:

Specific power
𝑊𝑊̇
𝑆𝑆𝑆𝑆 = (46)
𝐴𝐴𝑝𝑝

Output per displacement

𝑊𝑊̇
𝑂𝑂𝑂𝑂𝑂𝑂 = (47)
𝑉𝑉𝑑𝑑

Specific Volume
𝑉𝑉𝑑𝑑
𝑆𝑆𝑆𝑆 = (48)

Vigilada Mineducación
𝑊𝑊̇

Specific Weight
𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤
𝑆𝑆𝑆𝑆 = (49)
𝑊𝑊̇

Sin Límites
 TORQUE AND POWER

These parameters are important for engines used in transportation

vehicles such as boats, automobiles, and especially airplanes, where
keeping weight to a minimum is necessary. For large stationary
engines, weight is not as important.

Modern automobile engines usually have brake power output per

displacement in the range of 40 to 80 𝑘𝑘𝑊𝑊/𝐿𝐿 The Honda eight-valve-
per-cylinder V4 motorcycle engine generates about 130 𝑘𝑘𝑊𝑊/𝐿𝐿 an
extreme example of a high-performance racing engine.

One main reason for continued development to return to two-

Vigilada Mineducación
stroke cycle automobile engines is that they have up to 40% greater
power output per unit weight.

Sin Límites
 TORQUE AND POWER
Dynamometers are used to measure torque and power over the
engine operating ranges of speed and load. They do this by using
various methods to absorb the energy output of the engine, all of
which eventually ends up as heat. Some dynamometers absorb
energy in a mechanical friction brake (prony brake). These are the
simplest dynamometers but are not as flexible and accurate as
others at higher energy levels.

Fluid or hydraulic dynamometers absorb engine energy in water or

oil pumped through orifices or dissipated with viscous losses in a
rotor-stator combination. Large amounts of energy can be absorbed

Vigilada Mineducación
in this manner, making this an attractive type of dynamometer for
the largest of engines.

Sin Límites
 TORQUE AND POWER
Eddy current dynamometers use a disk, driven by the engine
being tested, rotating in a magnetic field of controlled
strength. The rotating disk acts as an electrical conductor
cutting the lines of magnetic flux and producing eddy
currents in the disk. With no external circuit, the energy from
the induced currents is absorbed in the disk.

One of the best types of dynamometers is the electric

dynamometer, which absorbs energy with electrical output
from a connected generator. In addition to having an accurate

Vigilada Mineducación
way of measuring the energy absorbed, the load is easily
varied by changing the amount of resistance in the circuit
connected to the generator output.

Sin Límites
 TORQUE AND POWER

Many electric dynamometers can also be operated in reverse,

with the generator used as a motor to drive (or motor) an
unfired engine. This allows the engine to be tested for
mechanical friction losses and air pumping losses, quantities
that are hard to measure on a running fired engine.

Vigilada Mineducación
Sin Límites
 AIR - FUEL RATIO AND
FUEL – AIR RATIO

Energy input to an engine 𝑄𝑄𝑖𝑖𝑛𝑛 comes from the combustion of

a hydrocarbon fuel. Air is used to supply the oxygen needed
for this chemical reaction. For combustion reaction to occur,
the proper relative amounts of air (oxygen) and fuel must be
present.

Air-fuel ratio (AF) and fuel-air ratio (FA) are parameters used
to describe the mixture ratio:
𝑚𝑚𝑎𝑎 𝑚𝑚̇ 𝑎𝑎

Vigilada Mineducación
𝐴𝐴𝐴𝐴 = = (50)
𝑚𝑚𝑓𝑓 𝑚𝑚̇ 𝑓𝑓

𝑚𝑚𝑓𝑓 𝑚𝑚̇ 𝑓𝑓 1
𝐹𝐹𝐹𝐹 = = = (51)
𝑚𝑚𝑎𝑎 𝑚𝑚̇ 𝑎𝑎 𝐴𝐴𝐴𝐴

Sin Límites
 AIR - FUEL RATIO AND
FUEL – AIR RATIO

Where:
𝑚𝑚𝑎𝑎 = mass of air
𝑚𝑚̇𝑎𝑎 = mass flow rate of air
𝑚𝑚𝑓𝑓 = mass of fuel
𝑚𝑚𝑓𝑓̇ = mass flow rate of fuel

Equivalence ratio 𝜙𝜙 is defined as the actual ratio of fuel-air to ideal

stoichiometric fuel-air:

Vigilada Mineducación
𝐹𝐹𝐹𝐹𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝐴𝐴𝐴𝐴𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
∅= = (52)
𝐹𝐹𝐹𝐹𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝐴𝐴𝐴𝐴𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎

Sin Límites
 Example

An automobile has a three-liter SI V6 engine that operates on a

four-stroke cycle, gives a brake ouput torque of 205 Nm at 3600
RPM. The engine is square (B = L) and B=8.6 cm. The mean piston
speed is 10.32 m/s

Calculate

1) 𝑊𝑊̇𝑏𝑏
2) 𝑊𝑊̇ 𝑖𝑖
3) 𝑏𝑏𝑚𝑚𝑚𝑚𝑚𝑚
4)

Vigilada Mineducación
𝑖𝑖𝑚𝑚𝑚𝑚𝑚𝑚
5) 𝑓𝑓𝑚𝑚𝑚𝑚𝑚𝑚
6) 𝑊𝑊𝑓𝑓̇
7) 𝐵𝐵𝐵𝐵𝐵𝐵

Sin Límites
 Example

An AVCO Lycoming four cylinder SI engine that operates on a four stroke

cycle engine produces 112 kW of brake power and 130 kW of indicated
power at 2800 rpm. The bore and stroke are related as B=1.242L. The
compression ratio is 8.5 and the average piston speed is 9.453 m/s. At this
condition, the air enters the cylinder with a pressure of 101.325 kPa and a
temperature 45°C and 0.00496 kg/s of mass fuel flow. Additionally, the
mechanical efficiency is of 86 %. This engine operates with 100LL aviation
gasoline and AF ratio for this gasoline is 14.2 and fuel heating value of
44000kJ/kg, and a combustion efficiency of 95%,

Calculate:
• mass air flow,

Vigilada Mineducación
• BSFC,
• Brake thermal efficiency,
• Indicated thermal efficiency,
• Volumetric efficiency

Sin Límites
 Example

An four cylinder engine that operates on a two stroke cycle

engine. The engines has 10.9 cm of bore and 12.6 cm of stroke,
produces 88 kW of brake power at 2000 rpm, the compression
ratio is 18.

Calculate:

Engine displacement
Torque
Bmep

Vigilada Mineducación
Brake work
Clearance of one cylinder
BSP

Sin Límites
 Example
A Piper Seneca I has a 4 cylinder Lycoming Engine that operates on a
four stroke cycle, with a stroke B = 13.02 cm y L=0.854B. Produces 149
kW of brake power in a 2700 RPM. The compression ratio is 8.7. At this
condition, the air enters the cylinder with a pressure of 106.830 kPa and
a temperature of 80°C. Additionally, the mechanical efficiency is of 78%.
This engine operates with 100LL aviation gasoline and AF ratio for this
gasoline is 14 and fuel heating value of 44820kJ/kg, and a combustion
efficiency of 97%
Calculate:
• mass fuel flow,
• BSFC,

Vigilada Mineducación
• Brake thermal efficiency,
• olumetric efficiency

Sin Límites