TECHNOLOGY – CALCULATING ENGINE CURVES
Table 1: F3 parameters for drag calculation
Item
Power rpm
Quantity 150kW 6500
Rolling tyre radius 0.28m ax
0g Vx 220km/h
Gear ratio value 3 mt
500kg
will not be accurate to within a tenth of a kW, this, together with race data, is good enough to obtain a solid idea of the car’s drag. To illustrate this, let’s walk through an example calculation with an F3 car. The F3 parameters we will be using are shown in table 1, above. Our ace in the hole here is
that engine power is torque x the angular velocity of the crankshaft. Working on the maths, this is seen in equation 1. From table 1, the torque
for our engine is 220Nm so, assuming a driveline efficiency of 90 per cent, the coefficient of drag is given by equation 2.
STRAIGHT TO THE POINT The best point to take for this calculation is at the end of the longest straight at maximum speed. At this point, most racecars are nearly balanced, so it’s a good starting point. The beauty about this quick hand calculation is that it gives you a reference point. This is
Figure 1: coastdown result plotting acceleration vs vehicle speed Another approach to take is
to conduct a coastdown test to determine drag. What you are plotting here is vehicle speed vs longitudinal acceleration. You should then have something that looks like figure 1, above. In this case, all you need to
do is convert acceleration to m/ s2 and speed to m/s, then export them to, say, Excel and Matlab and you are well on your way to determining the drag coefficient. I will leave it to the interested reader to figure out the details (hint to engineering students / junior data engineers, look at equation 1).
THE MAIN EVENT Now that we have drag, it is time to get on to the main event, which is determining the engine curve. The information we’ll
"Another approach to take is
to conduct a coastdown test to determine drag"
important for two reasons: 1) It gives a baseline to form the engine power around; 2) It is a valuable sanity check for manufacturer-supplied aeromaps. I have lost count of the number of times I’ve had to use this for the latter… As an aside, what do you do if the manufacturer- supplied aeromaps are radically different to the ones you have calculated? Well, until you have better information, scale it to the drag values you have calculated. It’s not perfect, but will get you by.
need from our data to do this is illustrated in figure 2. The principal channels you’ll
need are longitudinal acceleration
(ax), vehicle speed, rpm and gear selected. If you don’t have gear selected, don’t worry because determining the gear ratio is very straightforward. All you have to do is calculate engine speed / wheel speed and that will get you right in the ballpark. The trick, though, is to concentrate on the straights, hence why I’ve thrown in the lateral acceleration
74
www.racecar-engineering.com • May 2012 Equation 1
where, P
T = π2 ⋅ = power in Watts RPM = engine speed Equation 2
C A gr T r m g ax *
D = = Equation 3
CDA = drag V
t − t ⋅ ⋅ 3*20 / 0.280
T = tr (0.5 ρ⋅V ⋅C A m ax 2
= 0.937 ⋅
where, T = engine torque (Nm)
= forward vehicle speed (m/s) mt = total car mass (kg)
ax = longitudinal acceleration (m/s2) gr = engine speed / wheel speed for the required gear
rt = rolling tyre radius (m)
and steer angles so these can be readily identified. The other item we’ll need is the engine speed to wheel speed ratio of all the gears from the set up sheet. Using these factors, you will
be able to determine the engine curve, as follows:
• The first step is to export all the channels listed in figure 2 to a csv (comma-separated values) file. Concentrate on straight data only.
• Open this in Excel. • Once you have the file open,
identify where the gear position is and insert a column.
• In this blank column, next to the gear position, put in the appropriate engine speed / wheel speed ratio (there are a multitude of tricks you can use to automate this process, which can be readily found).
Once this is complete, we are ready to estimate the engine curve. The equation we are going to be using to do this is shown in equation 2.
D gr + ⋅ t ⋅
0.5*1.22 *(22 /3.6)05 /
2 0.5*1.22 *(22 /3.6)05
−55 9.8 00 2
⋅ )
EQUATIONS 60 ⋅
⋅
RPM P
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