Engine Equations

Question 1

Displacement (swept volume)

Answer 1

Vd = pi/4 x B^2 x S

Question 2

Clearance volume (combustion chamber volume)

Answer 2

Vc

Question 3

Compression ratio

Answer 3

rc = Vt / Vd = Vc+Vd / Vc

Question 4

Engine capacity

Answer 4

cc = Vd x n

n = number of cylinders

Question 5

cylinder volume at given crank angle

Answer 5

V = Vc + pi/4 * B^2 * (L + r + y)

L = connecting rod length
r = crank radius
y = distance from crank to piston

Question 6

Mean piston speed

Answer 6

Sp = 2 S N

N = rotational speed in rad/s

max speed just before the middle of the stroke (half way between TDC and BDC)

Question 7

Otto efficiency

Answer 7

otto = 1 - ( 1 / rc ^ gamma-1 )

Question 8

Draw the real and ideal PV diagram for an engine

Identify where EVC/IVC and EVO/IVO as well as the gross indicated work and the pumping work

Answer 8

draw it and check book

Question 9

Indicated work and power

Answer 9

Wi = Wig - Wp
(or = A - B from PV diagram)

Pi = Wi x n/nr

nr = 2, 4 stroke
nr = 1, 2 stroke

n - rotational speed of crank in rpm

Question 10

Break work and power

Answer 10

Wb = brake work measured on dyno

Pb = Wb x n/nr

Question 11

imep and bmep

Answer 11

imep = (Pi / Vd) x (nr / n)

bmep = (Pb / Vd) x (nr / n)

bmep/imep = Pb/Pi = mechanical eff

Question 12

AFR and equivalence ratio

Answer 12

AFR = ma/mf

Equiv ratio = AFRs / AFR

Question 13

sfc

Answer 13

sfc = mf / Pb

Question 14

Volumetric eff

Answer 14

Volumetric = (ma/rho) / (Vd * n/nr)

Question 15

Thermal eff

Answer 15

Thermal = Pi / mf * h

Question 16

Mechanical eff

Answer 16

Mech = Pb / Pi = bmep / imep

Question 17

Overal eff

Answer 17

Overall = Thermal * Mech

= Pb / mf * h

= 1 / sfc * h

Question 18

Brake torque

Answer 18

T = F * r

Question 19

Brake power

Answer 19

Pb = 2pi * N * T

N = crank rotational speed in rad/s

Question 20

Load

Answer 20

Power developed / max usable power

so at open throttle = 1/1 = 1
at half throttle = 0.5/1 = 1/2

Question 21

Draw the torque, power, and sfc characteristic for a enigne

Answer 21

See book