Mathematical Modelling
Angerole, Inc has developed an extensive suite of mathematical models to help explore and understand race car performance and response on the track.
So what's the difference between our mathematical models and this high dollar simulation you hear so much about? The answer is, our models are designed to reveal the underlying reasons for a car's behaviour on the track and do so in a comprehensible way. We replace complexity with simplicity, opaqueness with clarity.
We present some screen dumps below from some of our models that we hope, together with the notes, explain some of their capabilities. Clicking on any of the graphics will load one that is much larger and easier to see. If what you see interests you, please feel free to contact us to discuss its applications further.
Drag Analysis
It can be surprisingly difficult to get a straight answer to what should be simple questions:
Screens from one of our models that's designed to answer these sort of questions are shown below:
The dark blue in the graph above shows Thrust, meaning the drive available in pounds for a given amount of horsepower at a given speed. When the Thrust line is above the light blue Total Drag line, the car will still accelerate; where light blue and dark blue cross (meaning Thrust = Drag), that's your top speed.
Two drag lines, Aero and Rolling are included in the top graph. Rolling resistance, the amount the tyres stick to the road, is very significant and Angerole, Inc has accumulated substantial expertise in predicting it. The graph immediately above concentrates on this often ignored aspect of race car analysis. Here, the red line is rolling resistance in pounds, the blue is rolling resistance's proportion of total resistance.
Immediately above is a graph that shows drag and power increases with speed. For any given speed, this graph gives an easy and convenient way of finding out how much less drag or how much more power it will take to go 1mph faster.
In the case shown above, from the cursor legend, if the car tops out at 172mph, it would take 10.6lb less aero drag for it to do 173. It's important to understand that a figure like 10.6lb is not an absolute but a result of all the other factors that define the entire picture. What Angerole, Inc does is separate the number you need from the complexity.
Ride Height and Rake Management
Angerole, Inc mathematical models can be used to accurately predict ride heights and rake for given aero performance and car spring rates. Equally, they can be used to reverse engineer observed suspension deflection to determine, with good confidence, aero performance.
The graphs below are the output from one of our models. The software is written in such a way that multiple parameters can be easily adjusted to represent the desired final configuration. Please click on either graph to download a larger version.
The pair of graphs above show front and rear ride heights, and therefore rake, for an identically configured Formula Atlantic car. The difference between the two is due to torque weight transfer, the weight transfer from front to rear caused by drive axle torque. In the top graph you can see the ride and rake distribution under power while the bottom what you would get if you towed the car to the same speed.
We're bringing to your attention here how torque weight transfer, which is often simply ignored, is a very significant factor in dynamic ride and rake. The saw tooth pattern seen in the under power rake trace is caused by different torque multiplications as the car goes up the gears. A lesson that may be drawn is that one of the mechanisms for the way altering gear ratios can affect handling is that doing so will alter where rake is changed in a sequence of corners.
Our ride height model is capable of much deeper analysis that we have shown on this page. For instance, it will easily handle bump rubbers, air gaps and third springs along with rising rate geometry and non-linear aero performance. It's purpose and beauty is that it not only provides clear answers but makes it simple to explore and gain a feel for the magnitude of any given parameter or effect.
Load Distribution
Using the same base data, we present results configured in terms of axle load. The pair of graphs below are a partial indication of how load distribution is very substantially altered by many setup parameters and, especially, how the car is driven. Please feel free to click on either graph to download a larger version.
The difference between what we do and ordinary simulations is that Angerole, Inc models allow you and your team to easily see the effect and interaction of setup changes on the car's stance and grip potential. Our software tools encourage the active participation and involvement of your driver in learning why he feels what he does and, crucially, what to expect from a change.
If you would like to know more about our software products and how they can help your program, please feel free to contact us.