Hi BCP Folks,

I'm a long time lurker, but I had an epiphany that I want to share. It all started with me deciding I want bigger tires. I have 8.50 on my Cessna 140 now and I can brake hard enough that nosing over is possible. While trying to decide how big of tire I want (26" or 29") I realized I didn't actually know why bigger tires require better brakes. I heard talk of torque moments being larger but torque is a static force. I also couldn't find how much more braking is required for a given tire size. So hear it goes....

First, I'm talking rolling braking, not holding a static run up.
Second, I'm going to ignore drag for the time being.

Here's the situation: I land my 140 and as soon as I have weight on the wheels I apply as much braking as possible without nosing over and without skidding the tires. Lets say I have my original 600-6 tires on. Let’s say I came to a stop in 300 feet. During the braking period my brakes were doing work, they converted the kinetic energy of the aircraft into heat. The equation for Work is Work = Force x Distance. The Force is how much friction my brake pads can induce on the disk, which is related to how hard the caliper squeezes. The Distance is how many rotations my brake disc made(THIS IS THE EPIPHANY) times disk circumference.

With 600-6 (17" diameter) tires and some rough math, my wheels will rotate 67 times in that 300ft. That means my brake disk will do the same number of rotations.

Now I mount 29"; tires (29" diameter) and do the same math, my cool looking bushwheels only rotate 40 times in 300ft. My brake disks have the same amount of work to accomplish but now they must do it in 40% less distance. Looking at the formula Work = Force x Distance, Work stays the same, distance decrease, force must increase. And this is why better brakes are required.

Note - I'm using a short cut by considering the rotations to be a substitute for doing another step in the math. Distance = rotations x circumference of the brake disk. My disks are 7.5" diameter therefore Distance = 67rot X (7.5" x Pi) = 132ft. My brake calipers squeezed while 132ft of brake disk slid by VS 77 ft with 29"

To summarize bigger tires have larger circumferences, which reduces the effective distance the brake can act on, requiring better brakes or large calipers.

So I did some more math. If 600-6 tires my Cessna 140 came with equates to 100% braking. Then:
8.50 = 77%
26" = 65%
29" = 58%
31" = 54%
35" = 48%

In reality the brakes are probably oversized to account for worn brake pads or weak toes.

Is this correct? Was this obvious to everyone else and I missed out?

Disclaimer I'm a pilot not a mathematician. My Maule has double puck brakes. I had 8.50s until just recently when I went to 31s. With the 8.50s I could very easily hold the brakes and full throttle and not move. With the 31s I have to press the brakes much harder to prevent the plane from moving. Likewise on landing I had to be much more judicious with the brake previously with the 8.50s as I could brake much harder and either skid or nose over. With the 31s I haven't been able to apply enough brake peddle force to feel the tail coming up yet. Granted I'm still cautiously expanding the envelope but you can just feel the brakes don't have the same "effectiveness" as before.

My guess is the increased lever arm distance of the tire radius requires more friction force to overcome the same aircraft energy state. Yet the brakes are only capable of creating the same friction as before. Thus the requirements for double the friction surface or double pucks for using the bigger tires.

In MOST cases, larger tires are installed using the same brake discs. Basic physics suggests that braking effectiveness will decrease as a result.

That is, in fact, what happens, but if the math makes you feel better, so much the better.

MTV

I changed the wheels on my Maule MX-7-180 from single puck brakes with a 1/4" rotor to dual puck brakes with a 3/8" rotor. Then I changed my 8.50x6.00 tires to 31" Alaskan Bushwheels. The risk of nosing over with the tailwheel on the ground is less with larger tires because the center of mass at the tail is lower than the center of mass on the main wheels. The additional weight of the 31" bushwheels would have put too much strain on the single puck brakes and might have bent the master cylinder push rod with hard braking. Not only do the dual puck brakes remove this risk, but the brake pads last more than 4 times longer.