There are many reasons people want to measure the slip angle of vehicles. These include everything from developing models for electronic stability control systems to evaluating the performance of different compounds of tyre. But no matter what the data will eventually be used for, there’s one requirement everyone has in common—they want it to be accurate.
When it comes to measuring slip angle, accuracy means something very small indeed. ISO15037 recommends a maximum error of 0.5°, although most end users require much better accuracy than this because even a change of 0.5° in slip angle is significant in vehicle dynamics. But if you want to capture slip angle data with any confidence in its accuracy, it pays to understand how it’s measured and what you can do to minimise the sources of error that affect all GPS or inertial navigation slip angle devices.
The slip angle of a vehicle describes the ratio of forward and lateral velocities in the form of an angle and is normally represented by the symbol β. In other words it’s the difference between where something is pointing (heading) and where it’s actually going (track)—think of a plane landing in a crosswind or a rally car cornering. Both dual-antenna GPS and inertial navigation systems calculate slip angle by subtracting the object’s track angle from its heading. The first important thing to bear in mind therefore, is that slip angle data can never be more accurate than the heading accuracy—because one is based on the other.
You should also be aware slip angle accuracy changes with speed—something that often puzzles end-users. To calculate an object’s track angle, GPS and inertial measurement systems take the arctangent of the east and north velocities [atan(Ve/Vn)]. Bearing in mind these instruments measure velocity with a relatively fixed accuracy of, say 0.1 km/h, it seems obvious a small error like this is proportionally more significant at low speeds. That’s why slip angle accuracy improves with speed.
If you know the speed you want to conduct your slip angle tests at, you can calculate the expected accuracy of any system with the following function:
Other sources of error are down to the installation of the measuring equipment in the vehicle, or the device’s inability to compensate properly. That’s why engineers don’t mind spending time making sure an installation is good enough to capture the data they require. Measure twice, cut once as they say.
The same is true vertically because the roll rate of vehicles during dynamic tests can be as high as 1 radian/s. If the vertical distance between the point you’re interested in and the point you’re measuring from is 1 metre, it can affect the lateral velocity by up to 1 m/s. This in turn throws the slip angle off by nearly 3° at 72 km/h. For 0.5° accuracy it’s important to mount the instrument within 50 centimetres vertically of the point you wish to measure or your data will be inaccurate during dynamic tests.
This image shows the slip angle (β) as reported by the inertial sensor at two different speeds. Slip angle is the difference between the vehicle heading (represented by the vehicle’s x-axis) and its course over ground (track). The grey circles represent the possible error in the velocity measurement at low speed (v) and high speed (v’). So the true slip angle measurement may be anywhere within the relevant circle. The slip angle accuracy for each measurement is show by b and b’, and you can see how it decreases as the vehicle speed increases.
Road camber is one source of error that directly affects slip angle and can’t be controlled, but can be seen if the measurement device describes exactly how the vehicle body moves through space. This is one of the reasons inertial navigation based systems offer superior performance in real world testing—because they give users a complete and accurately timed picture of how the vehicle is moving in all axes.
So, achieving the slip angle accuracy you desire is down to more than just reading the specifications of a piece of equipment. At the very least it means selecting an instrument capable of measuring heading and velocity with enough accuracy for your needs—remember, as a rule of thumb, slip angle accuracy can only ever be as good as heading accuracy. And while slip angle accuracy will always improve with speed, by taking the time to install and configure equipment properly and calculating the expected slip angle accuracy based on the speed of each test, you can at least have confidence in the accuracy of the slip angle data you collect.
Download a more technical document on how to measure slip angle accurately, Slip Angle Accuracy (120802)
