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LONGITUDINAL

DYNAMICS Practical Works GROUP 1

Olivier KILO Saurabh SUMAN

1. Introduction

In this report the results and analysis from the Longitudinal Dynamics classwork has been briefly

discussed. Based on a given engine and vehicle data, calculations have been done on Excel to

calculate maximum speed, optimal gear box, fuel consumption at stabilized speed and MVEG cycle

respectively. Then the impact of gear box ratio on performance and consumption and the benefits of

stop & start systems have been analyzed. And finally the report concludes with a sensitivity analysis

by calculating the influence of different parameters on fuel consumption.

2. Gear Box Selection and Effect on Vehicle Performance

2.1 Input Data

Vhicle = Group 1

Segment B2

energy Gasoline

Curb Weight (kg) 900

Displacement (l) 0,7

Crr (kg/t) 7,5

Transmission efficiency 0,9

Scx (m) 0,7

Target of Acceleration for Take-Off (m/s) 3,5

2.2 Maximum Speed

Max Speed is mainly dependent on the maximum power delivered by the engine and the aerodynamics. As the vehicle speed increases the resistive forces increase.

Aerodynamic force which are proportional to square of vehicle speed becomes very high at high vehicle speed.

For our case the maximum speed achieved is equal to 163.33 km/h

2.3 Final Gear Ratio Adaption and Maximum Vehicle Speed Based on this maximum speed and maximum power engine speed, the final gear ratio was selected:

Final gear Ratio (L5opti) = 5 () = Vmax 1000

=

163.331000

5500= 29.7

/1000

To see the effect of final gear ratio on the maximum speed, it was recalculated for L5opti + 10%

and L5opti - 10%.

Top speed for short gear box: ( 5 ( 10%)) = 160

( 5 ( + 10%)) = 162.8

2.4 1st Gear Adaption & Take-Off

1st gear ratio was selected on the basis

of target take-off acceleration i.e. 3.5

m/s2. Based on maximum torque at

the launching RPM of 2500 RPM. Using

an iterative process the value of L1 was

calculated to get the desired take-off.

L1 = 8.36 km/h /1000rpm

2.5 0-120 km/h in last gear roll-on acceleration

Average Engine Speed (RPM)

Optimal = 3447, 17 RPM Short = 3890, 61 RPM Long = 3128, 58 RPM

2.6 Intermediate gear ratio For all the three gearboxes we have the first and final gear ratios. Now there are two ways to find the intermediate gears:

1. Arithmetic : the difference of gear ratios between a gear and the following is constant 2. Geometric : the quotient of gear rations between a gear and the following is constant

The intermediate gears were calculated by taking an average of the values calculated from above methods.

01000

2000

3000

4000

5000

6000

7000

0 5 10 15 20 25 30 35 40

En

gin

e S

peed

(rp

m)

Time (s)

0-1000m acceleration

Optimal Gear Box

Short GearBox (-10%)

Long GearBox (+10%)

2.7 0-1000m acceleration The 0-1000 m acceleration is done iteratively in order to know the current acceleration of the vehicle

with a 0.25s time step. The results show that the gear box has no significant influence on the time:

Gear Box Time for 0-1000m acceleration (s) Average Engine Speed

L5 opti 35.63 4700

L5 opti -10% 35.68 4635

L5 opti +10% 35.65 4492

However, the time spent in each gear is different from one gearbox to another, which ultimately

gives higher average engine speeds.

3. Consumption Analysis

3.1 Consumption at constant speed The following chart shows the fuel consumptions at constant speeds:

Speed (km/h) Gear Fuel cons with optimal GB (L/100km)

Fuel cons with short GB (L/100km)

Fuel cons with long GB (L/100km)

50 4 2.1 2.2 2.0

90 4 3.5 3.8 3.4

120 4 5.5 5.9 5.3

90 5 3.2 3.3 3.1

120 5 4.8 5.1 4.7

The long gear box gets better fuel consumption at constant speed (between 2 and 5% lower).

3.2 Consumption MVEG cycle Fuel cons with optimal GB

(L/100km and gCO2/km) Fuel cons with short GB (L/100km and gCO2/km)

Fuel cons with long GB (L/100km and gCO2/km)

Cycle Hot Cold Hot Cold Hot Cold

ECE 4.28 5.13 4.35 5.22 4.19 5.03 101.82 122.18 103.58 124.30 99.84 119.80

EUDC 3.77 3.88 3.87 3.99 3.68 3.79 89.69 92.38 92.22 94.98 87.62 90.24

MVEG 3.95 4.34 4.05 4.44 3.87 4.25 94.16 103.36 96.41 105.79 92.14 101.19

98.00

99.00

100.00

101.00

102.00

103.00

104.00

105.00

106.00

4.20

4.25

4.30

4.35

4.40

4.45

4.50

Short Optimal Long

CO

2 e

mis

sio

ns

(g/k

m)

Fue

l Co

nsu

mp

tio

n (

L/1

00

km)

Gear Box type

Fuel consumption and CO2 emissionsMVEG cold start

Fuel cons

This graph shows the evolution

of the cold start MVEG cycle

concerning fuel consumption

and CO2 emissions.

It also shows that the longest

gear box gives the best fuel

consumption.

3.3 Sensitivity Analysis Several sensitivity analysis were done in order to know the influence of each parameter on the fuel

consumption. Only one parameter is varying at once. (The reference case is highlighted in yellow).

Parameter Value ECE hot

Cold influence ECE

EUDC hot

Cold influence EUDC

Total Cold

Inertia class

910 98,12 19,62 87,57 2,63 100,35

1020 101,44 20,29 89,68 2,69 103,2

1130 104,91 20,98 91,83 2,75 106,12

Friction coefficient

6,5 100,74 20,15 88,13 2,64 101,87

7,5 101,44 20,29 89,68 2,69 103,2

8,5 102,06 20,41 91,2 2,74 104,45

SCx coefficient

0,66 101,22 20,24 87,49 2,62 101,67

0,7 101,44 20,29 89,68 2,69 103,2

0,74 101,69 20,34 91,87 2,76 104,72

Engine Inertia

0,108 101,14 20,23 89,63 2,69 103,02

0,12 101,44 20,29 89,68 2,69 103,2

0,132 101,82 20,36 89,74 2,69 103,4

The influence of the engine inertia is

negligible, even on the ECE part (see chart)

where there is more time spent in 1st gear.

The influence of friction coefficient is

important on both parts of the cycle

whereas the influence of SCx coefficient

only improves the EUDC part. However, the

parameter which seems to have the more

influence is the inertia class. One inertia

class makes a difference (almost 3%).

3.4 Influence of Stop & Start The graph clearly shows that the benefits

of stop/start system are due to the ECE

part. It is logical since most of the stops are

done in urban part of the cycle (ECE).

3.5 Fuel consumption reduction By changing these parameters the fuel consumption is decreased by 0.5L/100km (=11.9 gCO2):

Gear Box St/St Tires SCx Inertia Class

Old value Optimal NO 7.5 kg/t 0.7 1020

New Value Long YES 6.5 kg/t 0.66 910

gCO2 gain alone 2.01 4.25 1.29 1.55 2.89

gCO2 cumulated 2.01 6.26 7.55 9.1 11.99

4. Conclusion Based on the calculations and analysis, following conclusions can be made:

1. Aerodynamic forces have a major impact on maximum achievable speed of a vehicle for a

given engine.

2. First gear ratio is calculated on the basis of desired maximum take-off acceleration.

3. With a short gear box acceleration is higher in 0 to 120 km/h speed range but the engine

runs at higher RPM.

4. For 0-1000 m acceleration, the gear box selection does not have significant effect on time,

but the average engine RPM for optimal gear box is the highest because the time spent on

different gears for the three gearboxes are different.

5. The long gear box gets better fuel consumption at constant speed (between 2 and 5% lower).

6. The longest gear box gives the best fuel consumption for MVEG cycle.

7. Fuel consumption can be improved substantially with better aerodynamics and inertia class.

8. Stop start is effective in reducing consumption in the urban (ECE) part of the MVEG cycle.