Alright, let's do some analysis here. First off, let's get one big thing out of the way.
This is not a quantitative stiffness analysis.
We do not know enough about the torsional behavior of the vehicle to get a hard, reliable number for the torsional loads a vehicle experiences on track. So we're going to pick a reasonable number, and hold it constant through multiple tests and see how the results compare.
What this means is the numbers do not match up to the real world. They are only useful for comparing between tests.
First off, we'll apply 1000 ft-lbs to the rear four mounting points of the cage. These loads are evenly distributed between the points, but the points are not constrained to each other. They can move around naturally.
The front two mounting points will be fixed. We will measure displacement of the lower left roll cage mounting plate, and use that to calculate an angular deflection, which we can use to compare different configurations.
The first test is a simple 6-point cage with a crossed main hoop brace, a double crossed main hoop, and full length harness bar. This is the lightest, simplest cage design, and will be the starting point for this study.
Deflection- 2.49°
Stiffness- 402 lb-ft/deg
Weight- 99.5 lbs
Next, let's add FIA style door bars:
Wow. Okay, door bars really help torsional stiffness across the car.
Deflection- 0.47°
Stiffness- 2146.6 lb-ft/deg
Weight- 125.6 lbs
That's an improvement of over 400%. So we're definitely adding door bars. Now, let's add some beams between the bottom of the rear hoop and the rear shock mounts. These types of bars are common on flexy unibody cars.
Deflection- 0.43°
Stiffness- 2321.9 lb-ft/deg
Weight- 134.05
So for an additional 8.5 lbs we pick up another 8% stiffness. Not bad.
Many series allow two additional chassis points on the firewall to protect the driver's compartment from wheel intrusion in accidents. Let's add those and see how much stiffness they add.
Deflection- 0.36°
Stiffness- 2758.1 lb-ft/deg
Weight- 135.52 lbs
An extra 1.5 lbs (neglecting landing plates, of course), and we gain another 18%. Pretty good for the negligible weight, and considering they're really there for safety.
Now, what about the different between FIA bars and NASCAR bars? Everyone knows NASCAR bars are better at protecting the driver in broadside impacts since they arc out away from the driver, but how do they affect torsional stiffness?
Deflection- 0.30°
Stiffness- 3297.7lb-ft/deg
Weight- 145.02
So they weigh an extra ten pounds more than FIA bars, but they add almost 20% more torsional stiffness! Sounds like a good deal.
This sort of iterative analysis is a bit of insight into how we design. Torsional stiffness is just one of many things to consider when designing a cage, but you can see here why certain things are the way they are.
Jake