It has been a while since we posted a math’s feature, and so here we go looking at engine power output (BHP) thanks to the joy math channels
We often discuss “non-intrusive testing” and the following is a perfect example of this philosophy using an accelerometer to determine engine power output
This test requires only one probe in the form of a TA143 3-axis accelerometer (Acc) from our NVH kit here
https://www.picoauto.com/products/noise ... h-overview
The first step in the process of engine power output calculation is the acquisition of the accelerometer calibration factor (ACF). This process is automated in our Pico Diagnostics NVH software, however, for this test procedure we are using PicoScope 7 Automotive
The ACF acquisition process is very straight forward indeed and requires the
X-axis of the TA259 NVH interface to be connected to a PicoScope channel (See image and text below)
- Image 1
ACF acquisition procedure
1. Connect the TA143 3-axis accelerometer to a TA259 NVH interface
2. Connect the X-axis output of the TA259 NVH interface to PicoScope (Above we have used channel C)
3. Set the scale of your chosen channel to x10, the input range to +- 2V (DC coupled) and a timebase of 5 sec/div (Total buffer time = 50 seconds)
4. Hold the accelerometer with the screw thread hole positioned vertically down and start recording.
5. After 20 seconds, turn the accelerometer over so that the screw thread hole is now pointing vertically up.
6. Continue recording for a further 20 seconds and then stop the capture
7. Activate lowpass filtering and set to 10 Hz for your chosen channel
6. Align both signal rulers on the captured signal as shown above and record the delta (Δ) measurement
7. Divide the Δ measurement by 2, to obtain a value typically of 0.101 mV
8. Divide 9.81 (Acceleration due to gravity) by the value obtained in Step 7 to arrive at the Accelerometer Calibration Factor (ACF)
E.g., 9.81 m/s/s / 0.101 = 97.129 m/s/s/V. (
Record this value for later use)
Set-up
With the ACF acquired, attach the Acc to the driver’s seat frame, vertically with the screw thread facing forward as in the image below. We are interested in measuring the X-axis only; the fore-aft movement of the vehicle under acceleration
- Image 2
1. Connect the TA143 3-axis accelerometer to a TA259 NVH interface
2. Connect the X-axis output of the TA259 NVH interface to PicoScope (In our test we have used channel C)
3. Set the scale of your chosen channel to x10, the input range to +- 2V (DC coupled) and a timebase of 5 sec/div (Total buffer time = 50 seconds)
4. Drive the vehicle to a straight / level road and
roll to a halt rather than brake to a stop. Braking will result in “nose diving” and the vehicle posture may not return to its natural ride height
5. With the vehicle at rest, start the recording but
do not accelerate for approximately 5 seconds. During this period, we need to capture the DC value of the accelerometer relevant to the vehicle posture and acceleration due to gravity (This is referred to as the DC component of the accelerometer) We also use this significant value at the end of the road test to qualify the vehicle has returned to its natural ride height identified at the start of the test run. If we allow 5 seconds at the end of our test run to confirm the ride height pre and post power test we have approx. 40 seconds in our buffer to carry out a WOT acceleration test
Road-test (now for the fun part)
1. Follow all relevant safety precautions and road traffic laws
2.
Do not run this test alone, one person is the designated driver who will be instructed by the laptop operator
3. If applicable, set the vehicle driving modes to Sport or “I want my mommy” mode (in the case of Tesla)
4. Turn off Traction control VSC / ESP if applicable and be aware of the implications of deactivating these systems (The vehicle will inform the driver of such)
5. With the scope running accelerate the vehicle at WOT such as to achieve maximum power at the specified rpm
6. Remember the purpose of this test is to determine the power output of the engine and so manual upshifting must take into consideration the specified rpm at which peak power is acquired (Do not upshift too early)
7. Be conscious you have 40 seconds of recoding time and during this period you will have to brake the car to near rest
8. Allow the vehicle to finally roll to a halt and note the DC component voltage of the accelerometer which will hopefully match the value obtained prior to the test run
9. Stop the scope and save your data (See below)
- Image 3
Above I have included a road speed math channel derived from the ABS tooth count (48 teeth per wheel revolution) to help explain the response from the accelerometer (Channel C) More information on road speed via math channels can be found here
viewtopic.php?p=96821&sid=b2891430de61e ... 573#p96821
Note how the vehicle accelerates rapidly from rest (vehicle squats) where you experience that “
pushed back into your seat” feeling, followed by a recovery of the vehicle posture during the upshifts
We then have an over-run period of little or no acceleration followed by a gentle increase in road speed (I may have been trying to fill the buffer with data at this point)
Finally, the brakes are applied to reduce road speed and bring the vehicle to a rolling halt.
Note how the accelerometer value at the start of the test with the vehicle at rest = 936.8 mV (DC component) does not quite match the value obtained as the vehicle rolls to rest! This may well have been due to an inclination in the road surface or, insufficient time for the ride height to return to its natural position. Where possible (to prevent errors accumulating in the math channel) try to bring the vehicle to rest in such away as to accurately match the value obtained at the start of the test run
So how do we calculate BHP from the above data?
Here is the math channel returning BHP for the accelerometer data captured on channel C above
1.341*
97.129 *
97.129 *
1765/1000derivative(integral((
C-0.9368)*integral(
C-0.9368)))
Using a combination of conversions (Watts to BHP) calculus (Integral & Derivative) accelerometer calibration factor (ACF) and DC Component of the accelerometer at rest, we can graph engine power
1.341 converts Watts to BHP
97.129 (ACF^2) converts the voltage output (measured by PicoScope) into Acceleration
1765 is the
weight of the vehicle during the test run (kg)
1000 converts Watts to kilowatts
“Derivative” defines to rate of change with respect to a variable (e.g., “time”)
“Integral” (area under the curve)
“C” is the PicoScope channel connected to the accelerometer
0.9368 V is the DC Component of the accelerometer (Volts)
Please do not dwell on the math’s above and except that the formula above will return engine power assuming your Channel letter (“
C” above) ACF (
97.129 above) DC Component (
0.9368 V above) and vehicle weight (
1765 kg) are accurate and entered correctly
- Image 4
Above we have the Power BHP math channel returning an average peak of approx. 164.5 BHP and a 0...60 mph time of 7.51 seconds
The vehicle in question is a BMW 320 d Auto X Drive Touring which is specified at 181 BHP and 0…
62 mph in 7.5 seconds; so why the difference between measured and specified BHP?
Vehicle manufacturers quote engine power based on engine dyno results and
not a chassis dyno. In other words, the engine is run purely on a dyno and not connected to the transmission /vehicle. Therefore, there are no losses to account for and the true engine power output can be acquired
With our test above, the engine is subjected to load and therefore losses such as the Auto Transmission, X-Drive-train, rolling resistance of the tyres, traction loss, vehicle weight, wind resistance, road surface undulation and coefficient of drag.
As a general rule of thumb, we lose 15% of the specified engine power via the aforementioned items
Therefore: 181 BHP x 15 / 100 = 27.15 (BHP loss)
181 – 27.25 = 153.75 BHP (Expected BHP measured on the road)
The above calculation highlights the variables to consider during the road-test and the accuracy of the data entered, all of which have a huge influence on the acquired figures
Have I been a little ambitious with my peak measurement point for BHP?
Note below, peak power is 153.3 BHP in 2nd gear and appears to be an average throughout the road test (look between 4th & 5th gear) Perhaps this is a more desirable and accurate measurement point given the load on the engine will be at its greatest from rest, once we are rolling the load is reduced, however we then need to factor in wind resistance and drag
- Image 5
Whatever and wherever you decide to measure, keeping your road tests and measurement criteria identical will return accurate
relative measurements on which to base your diagnosis and qualify any repairs. (Be mindful about variables such a vehicle weight and consider fuel level and cabin occupant weight!)
Moving onto additional measurements, below we have added engine speed via the crank sensor signal, but not using “Crank(A,60)” math channel due to the low sampling rate. (Remember math channels favor a high sample count/rate) Instead we have introduced a “Low Pass filter” into a “Frequency” math channel “(60/60LowPass(freq(A),8)” to smooth out the aliasing we see at high engine speed and therefore plot the “Trend” of the RPM which will help with the additional calculations to follow.
- Image 6
So why do we want to graph engine speed? Well, if we have engine speed and power, we can calculate Torque!
The formula for Torque requires engine Power to be expressed in Watts and
not BHP
Engine Torque (Nm) = Power (Watts) / x ω where ω is the rotational speed in radians/s
The math channel is written as follows:
97.129*97.129*
1765*derivative(integral((C-
0.9368)*integral(C-
0.9368)))/(60/60*(LowPass(freq(A),8)*2*3.14159/60))
97.129 (ACF^2) converts the voltage output (measured by PicoScope) into Acceleration
1765 is the
weight of the vehicle during the test run (kg)
“Derivative” defines to rate of change with respect to a variable (e.g., “time”)
“Integral” (area under the curve)
“C” is the PicoScope channel connected to the accelerometer
0.9368 V is the DC Component of the accelerometer (Volts)
The above will return engine power in Watts………
(2*π/60)*RPM will return engine speed (RPM) to angular velocity in radians per second (rad/s)
- Image 7
Note above the Engine Torque value obtained (292 .7 Nm) at our average peak power (153.3 BHP)
The maximum Engine Torque achieved was approx. 338 Nm with the specification being 380 Nm @ 1750-2750 rpm. Remember once again that specified Engine Torque is calculated using an engine dyno not a chassis dyno. The engine torque figures above incorporate engine power with approx. 15 % loss which of course will reduce torque by the same amount. If we add 15 % to our maximum engine torque figure of 338 NM we arrive at:
338 Nm x 15 / 100 = 50.7
338 + 50.7 = 388.7 Nm (Specification 380 Nm)
Working with the above data, it occurred to me we have engine and road speed data thanks to the crank and ABS sensor signals. If you then incorporate the differential ratio, you have transmission input and output shaft speeds and if you have these, you can calculate gear ratios!
For example: Gear ratio = Input speed (RPM) / Output speed (RPM)
Given we know engine speed (RPM) using the math channel “(60/60LowPass(freq(A),8)” we have the transmission input value ready to go.
We know road speed (MPH) using the math channel 1.03*3600/63360*2*3.1416*13.016*freq(B)/48 therefore we can modify this formula to return wheel frequency (Revolutions per second) multiply by the differential ratio (2.81) to find propshaft/transmission output frequency (Hz) and then multiply again by 60 to convert to RPM
The math channel to determine Propshaft/transmission output speed (RPM) from ABS tooth count looks like this “freq(B)/48*2.81*60”
To find gear ratios we the divide the transmission input speed by the transmission output speed by joining the above math channels together as below:
60/60*LowPass(freq(A),8)/(freq(B)/48*2.81*60)
- Image 8
As you can see above the gear ratios are displayed clearly except of course for 1st gear (from rest) where we have to factor in torque convertor slip and multiplication. With that said, from 2nd gear onwards the accuracy is near identical to the specifications below (ZF 8 Speed Transmission)
- Image 9
All-in-all the above techniques demonstrate how measuring engine Power and Torque for
any vehicle (petrol, diesel or electric) can be performed in a non-intrusive fashion so providing another string to your bow during diagnosis and qualification of repair.
Please note, the tests above return a relative measurement for indication of Power and Torque and be aware of the numerous variables that can creep into the obtained results between testing. (One of which might be the weather!)
I will follow up this forum post looking at Hub Torque, Wheel Torque, and Braking Force which make for an interesting twist on the above Engine Power and Torque figures
It is mind blowing when you think we have gone from this, to this…..
- Image 10
To this…….
- Image 11
I must say a big thank you to the team here at Pico, naming Barney, Ben and Martyn and a HUGE THANK YOU to Martin Rubenstein for his assistance with this adventure that started in the summer of 2018!
I hope this helps, take care…….Steve