How do vacuum boosters scale their assistance?

I was reading this thread: https://grassrootsmotorsports.com/forum/grm/1969-mustang-restomod-brakes-brake-experts-needed/272928/page1/

...and the notion of a booster with a particular multiplier was raised. This piqued the back-of-mind question I've long had about how vacuum boosters provide a (fairly?) proportional boost to input pressure rather than just a fixed force based on the atmospheric vs vacuum pressures and the area of the diaphragm.

So, how does that work? I tried a few searches, a few videos, and had a very frustrating conversation with ChatGPT, which never seems to know even the bits I do about technical topics.

I'm guessing there's some sort of mechanism related to the deformable "reaction disc" in the pushrod stack that balances flow through from the atmosphere into the pressure side and from there into the vacuum side, but the operative word there is, indeed, guessing.

I know the answers are forthcoming, but I was shocked to learn that a certain newer Honda had a 10:1 force multiplication in the booster.

Holy jeez that is a lot!  I guess they aren't worried about being able to brake if the engine stalls, anymore.

In reply to Pete. (l33t FS) :

Some NB2 Miatas (2001-05 non-Sport and Sport with ABS, except for MSM) have a 9.7x booster.

If the engine stalls, you've got at least some vacuum in the booster to help you stop. Just don't keep going down the mountain pass with a dead engine and the transmission freewheeling :)

Video should start at the relevant vacuum booster bit.  The key is the springs in the valve, to create a negative feedback loop, you push on the brake pedal, the booster pushes too, which reduces how much force is relatively coming from the pedal, which reduces how much the valve opens, and it's all linear.  Power steering systems are similar except it's a torsion spring and not a coil spring.

The whole video is gold, though, especially if you dislike overly padded YouTube videos.  It's satire and also educational.

Pete. (l33t FS) said:

The whole video is gold, though, especially if you dislike overly padded YouTube videos.  It's satire and also educational.

Pretty much everything on SuperFastMatt's channel is worth watching.

Haven't watched it yet but plan too. I find most cars to be over boosted. I've wondered if it's possible to change that without swapping parts...

Mind like a steel sieve... I know I've watched that video, and look forward to learning all over again... Thanks!

Glad the video explanation helped refamiliarize you with how vacuum boosters work. Sometimes a refresher is all we need to jog the memory. 

I can tell you that if the reaction Disc thingy is missing or out of place that the brakes will lock up at the slightest hint of pushing on the pedal.

(At least in a 2nd gen rx7).

Man I'm glad I didn't have to jump in and expose how little I know about vacuum boosters. Pete's summary of the moving cartridge assembly is spot on.

I'm learning to hate vacuum brakes. They can be wildly inconsistent, especially with a big cam or if you brake and gas at the same time. I'm in the process of deciding it I want to retrofit manual brakes on the car to eliminate all the booster issues on track.

I wonder if one of those electric boosters will fit? Seems pretty tall for the space I have, but the booster is gigantic anyways. Plus I get rid of one or more random hoses in the engine bay.

In reply to theruleslawyer :

It doesn't look like it takes up much more diametrical room, but it does add a bit of length.

Still a lot shorter than Hydroboost, though, and no hoses.

I saw a tubeframe that had floor mounted pedals, and a balance bar adapted onto a Hydroboost.  In a Corvette(ish) the ends of the masters practically rubbed the back of the tire.

In reply to theruleslawyer :

An electric vacuum pump could work with your current setup as another option, should be simple to setup and you should be able to find oem parts at a u-pull yard.

adam525i said:

In reply to theruleslawyer :

An electric vacuum pump could work with your current setup as another option, should be simple to setup and you should be able to find oem parts at a u-pull yard.

It might, but I think I might have a leaky reaction plate (or whatever you call the cabin side valve) Its contributing to the problem. I'd hate to spend money and find that it's still an issue. Plus gaining a little clearance for cylinder 7 access would make my life easier.

While we're on the topic, can anyone explain to me why I was able to swap out the puny stock calipers on my 05 Mustang GT for 6-piston Brembos with no change to the MC or booster and maintain a stock-like brake feel and boosting? I did it because the forums told me it would work, and it did, but I'm struggling to understand why. Seems like it's moving a lot more fluid now.

In reply to Tom_Spangler (Forum Supporter) :

Increasing pad surface area in contact with the rotor increases how much heat the pad can absorb during a braking event.

But, increasing pad arc length without spreading out the clamping force from the pistons along the new length can lead to NVH issues as well as poor pad wear.

So we redesign the caliper to use multiple pistons, to distribute the clamping force on the longer pad. These multiple pistons are smaller diameter than the "big single", and since volume varies with diameter squared, we choose the new piston diameters such that the total volume of brake fluid consumed is the same between a big single and an equivalent multi-piston.

example: the area of a single 60 mm piston is (ignoring the pi/4 since it cancels out) 3600 mm^2.

if I wanted to use a two-piston caliper with equal diameters, each piston would be 1800 mm^2, and the diameter of each piston would be sqrt(1800), or about 42.4 mm.

in your case, IIRC the OE S197 caliper was a 2 piston with 42 mm diameters, so the 3600 mm^2 area is close enough for this example. To do this with 3 pistons per pad, even making them 3 unique diameters, it's just math:

3600 = 1000 + 1200 + 1400

In this case the piston diameters would be

sqrt(1000) = 31.6 mm

sqrt(1200) = 34.6 mm

sqrt(1400) = 37.5 mm

now, you may be wondering why I'm only counting pistons on one side of the rotor. That's because the total pad movement, therefore total fluid volume, is the same between a sliding caliper and an opposed piston aka fixed caliper.

Consider there's a 1mm gap between pads and rotors. In a sliding caliper, the piston travels 1 mm to make inboard pad touch rotor, then the piston pushes out another 1 mm to make the caliper slide inboard to pull the outboard pad 1 mm to contact the rotor. Total piston travel 2 mm.

Now consider fixed mount, opposed piston caliper. Same 1 mm gap between pads and rotor. Inboard pistons move 1 mm to put inboard pad in contact with rotor. Outboard pistons also move 1 mm to put outboard pad in contact with rotor. Total piston travel = 2 mm, so total fluid volume consumed is the same.

Wow, thanks! That helps a lot.

That's why manufacturers like Wilwood publish "piston area", so you don't have to math :) 

The pistons I have seen in 6-pots were TINY.  I've also never seen 6 pots that didn't have differential bores (prevents pad taper).  I know all four Brembos on my Volvo (4 pots only because I'm a chud) have differential bores, while the RX-7 4-pots were equal sized bores, along with all of the Wilwood 4-pots that I have.  I am pretty sure you can get differential bore 4 pots from Wilwood but the pads are so short in length it may not matter as much, compared to the benefits of not having side specific calipers.

Which bugs me when people swap application-specific calipers from one car to another, moving it from rear caliper to front caliper or vice versa.  The differential bores will be backwards if you do that.

Where I was going with this, is I also wonder how much caliper stiffness plays a role.  A good fixed caliper with a bolted in bridge or a monobloc design will have less caliper flex than a sliding caliper.  Some sliding calipers you can HEAR flexing when you apply the brakes!  Less flex would allow more piston diameter for the same pedal travel, I'd think.

Great input and updates.

Thanks all