How do you calculate the effect of a brake booster?

This is far more information than anyone needs, but sometimes it's useful to lay it all out. Here's the real question:

Is there any way to figure out the amount of assist from a particular booster - or the relative assist from two different boosters? For example, if the Miata uses a 7" booster and the MG uses a 6" one, does that mean the MG will provide 6/7ths of the assist? Or 36/49ths? 18/25ths? Or is it more complicated than that and the internal design has an effect?

Okay, now the rest of it. Feel free to ignore if you're not interested.

As part of the LS-powered MG project, I'm overhauling the brakes fairly comprehensively. It'll have Miata parts at each wheel, that part is easy. The problem is at the pedal. The car originally had unassisted brakes. Yes, well, it also had something like 80 hp, tires with no grip by modern standards, and drums in the rear that don't take much line pressure. So I want power brakes.

I've picked up a servo setup from a later MG that fits beautifully. It has a 3/4" master on it by all accounts. I'd prefer something bigger, at least as large as the 7/8" master on the Miata or even the 15/16" master on the later Miatas. Turns out there's a 1" unit available from Wilwood that fits very well - but only a 1". The need for a remote-reservoir dual circuit power-compatible setup kinda cuts down on the options. If I could find a 15/16" that would work, that would be perfect.

Here's what my calculations have come up with. The numbers are the amount of pedal pressure for 500 psi of line pressure, and the amount of pedal movement for 0.5 cubic inches of fluid movement. I do need to double-check the pedal ratio measurements for the MG parts, but they should be pretty close. These are all unboosted, mechanical ratios only.

• MG pedal, MG master: 50.8 lbs, 4.91"
• Miata standard setup: 73.3 lbs, 3.41"
• Miata Sport setup: 84.2 lbs, 2.97"
• MG pedal, 1" Wilwood master: 90.4 lbs, 2.76"

The Miata numbers are in there for reference, because I know what they feel like. Only the two MG pedal setups are an option. But where I'm stuck is on the role of the booster. Is there any way to figure out the amount of assist from a particular booster - or the relative assist from two different boosters? For example, if the Miata uses a 7" booster and the MG uses a 6" one, does that mean the MG will provide 6/7ths of the assist? Or 36/49ths? Or is it more complicated than that and the internal design has an effect?

As a point of reference, I have the Miata Sport setup on the Targa car and both Janel and I like the feel. I do have an idea about an interesting potential front caliper for the MG that would let me run slightly larger pistons, and there's a bolt-on option for larger pistons in the rear from later Miatas to ease up on pedal pressure a bit if required. The car will have an adjustable proportioning valve as well.

I should also mention that the MG is not a track car and will likely not have enough heat management capacity in the brakes to deal with hard track punishment. I'm okay with that.

Correction. I measured the MG brake pedal again, and found out the stock unit is 13/16". So here are the new numbers:

• MG pedal, MG master: 57.87 lbs, 4.32"
• Miata standard setup: 73.3 lbs, 3.41"
• Miata Sport setup: 84.2 lbs, 2.97"
• MG pedal, 1" Wilwood master: 87.7 lbs, 2.85"

I think I'll go with the 1" Wilwood master and mess with caliper piston sizes if I have a real problem with the amount of pressure required. But I still want to know if brake boosters can be generalized based on size, or if you have to somehow measure their assist with x inches of vacuum.

Interesting. What say you, O Angry Corvair?

what's magic about 500psi line pressure? is that the pressure required to make enough brake torque to pull a 1g decel or something?

to keith's question: boost ratio is determined by some components internal to the booster, and is not related to the diameter of the diaphragms.

total amount of helping force available from the booster is what's dependent upon the diaphragm area(s).

i'd start at the corners and work back to the pedal, like this:

how much weight transfer is there at 1g (or whatever useful max you choose, based upon tires selected)? so, what are the front and rear weights at 1g decel?

how much brake torque do you need to generate 1g at the front and at the rear?

what's the friction level of the pads you're going to use? (that's kind of a trick question, as there's not a pad out there that gives the same friction for all operating conditions)

with your chosen calipers, rotors, pads, and tires (size and compound), how much line pressure is required to pull 1g (or whatever your target decel is)?

what combination of master cylinder and pedal ratio will give you that pressure at a reasonable (your judgment on definition of "reasonable") pedal force?

500 psi brake pressure is a constant, allowing me to compare how the amount of pressure required would change with the various combinations, all else being equal. It doesn't really matter what that chosen pressure is, it just lets me look at the numbers and say "ooh, I'd have to push 75% harder with that setup". Same with the 1/2 ci of fluid movement, it's simply a constant in the equation.

The calculations of weight transfer and the like aren't something I can do now. I don't know where the CG will be on this car, and I don't know the total weight or distribution. And of course, it's basically impossible for a non-OE to come up with friction charts from a tire manufacturer. I'm thinking it's going to be in the same ballpark as an LS1 Miata, perhaps with a little more rear static weight bias. Thus my comparisons with the Miata braking system. I was hoping I could work on relative numbers instead of starting from scratch.

Looks like I'll be using ye olde experimental method. I really only have one variable at the moment, which of the two master cylinders to use. Without knowing how much assist we're going to get from the MG booster, it's a crapshoot on how much pressure will be required at the pedal.

Anyhow, back to a couple of your statements for educational purposes.

boost ratio is determined by some components internal to the booster, and is not related to the diameter of the diaphragms. total amount of helping force available from the booster is what's dependent upon the diaphragm area(s).

I'm not sure I follow the difference between boost ratio (the ratio of the booster input pressure to the pressure exerted on the master cylinder pushrod?) and total amount of helping force (the total amount of extra pressure the booster can supply?).

Keith wrote: I'm not sure I follow the difference between boost ratio (the ratio of the booster input pressure to the pressure exerted on the master cylinder pushrod?) and total amount of helping force (the total amount of extra pressure the booster can supply?).

booster is a force multiplier, so if you replaced "pressure" with "force" in your responses above you'd be exactly right on both.

so yeah, the boost ratio is the amount the input force is multiplied to get the output force.

Cool, thanks.

I'm back

So, according to the 1990 Miata factory manual, with 44 lbs of force on the pedal and no engine vacuum, line pressure should be between 156-171 psi. With 19.7 in of vacuum and the same pedal force, the line pressure should be 754-796.

So, using the upper end of those two numbers, that tells me the Miata booster has a boost ratio of around 4.6. Do I have that right?

Unfortunately, the MG service manual doesn't include this kind of information. I wonder if I could find some way to bench test the servo? Hmm... or I could bolt it together and see how it works.

Oh, and in my numbers above, my 500 psi line pressure is really 250 psi. I ignored the fact that there are two circuits involved. I guess the fluid movement is also for 1 cubic inch of fluid, not 1/2 as well. Doesn't really make any difference for my comparative purposes, but just to acknowledge.

i'd say the ratio would be somewhere between (754/156) and (796/171), so for our purpose i'd call it 5:1.

does the miata booster fit in the same space as the MG booster? if so, and if the miata has an aluminum MC body with a plastic reservoir, you could remove the miata reservoir and make a pair of inserts / hose adapters for the MC and then mount the reservoir remotely.

I'm pretty sure the Miata booster won't fit. It's an inch larger in diameter from what I remember. But I think I need to make 100% sure. I'll bring one home tomorrow.

I've been thinking along similar lines as your suggestion. Of course I know where to get a 15/16" master - off a Miata! The bolt pattern is wrong, but I think there's enough meat in the stock flange to make it work.. It does indeed have a removable plastic reservoir, which could be turned into a removable setup. This also means I have a 7/8" option, which suddenly gives me the possibility of 13/16", 7/8", 15/16" and 1" masters to play with, as long as I'm willing to do a bit of work.

Looks like the pushrod used on the Miata is slightly longer than the MG one - about 1/4" or so. Is this something I should be concerned with, or is it just a matter of adjusting the length of the pushrod pre-booster to take up the amount of play?

pushrod should be long enough to not rattle around, but short enough to allow full release of booster.

look at packaging the miata booster, even if you have to fab a bracket to hold it in place. like you said, it gives you a lot of MC options, cheap, and you know they're all properly sized for the calipers you're going to use.

It's the obvious solution, isn't it? Duh. My knee-jerk reaction was "it'll never fit, it's too big". But it's worth trying, so I took a couple of Miata boosters home last night.

They're about 1.5" larger in diameter than the MG one, and that's a problem. After some light tapping with a 2 lb sledge on the body and some new mounting holes in my pedal box, I was able to get it in. There is about 1/4" of clearance between the valve cover and the booster, but it fits! I can solve the valve cover problem with some creativity. I'm pretty sure it'll clear the hood but the vacuum fitting will need some realigning.

By the way, looks like Miatas came with 4.75, 6.4 and 9.7:1 brake boosters over the years. All the same 8.5" diameter, but the 9.7:1 unit is thicker and I suspect there's a second diaphragm in there. If anyone wants all sorts of Miata brake interchange trivia, I can provide quite a data dump.

Thanks for the help, Angry. Much appreciated.

Keith wrote: Thanks for the help, Angry. Much appreciated.

hey, that's one of the reasons i'm here.

May I thread-jack and ask a question about the vacuum line for a brake booster?

I'm switching from a single throttle body to a quad throttle setup and so I bought a vacuum manifold to supply vacuum to the brake booster. The oem intake manifold has a 3/8" fitting for the brake booster's vacuum. My vacuum manifold has this size at one end and four 1/8" npt fittings along the side. My throttles can be plumbed for 1/8" or 1/4" vacuum hoses.

Will my brake booster still work relatively close to stock if I stick with the four 1/8" lines going into a 3/8" fitting?

bump for help please

I don't think the amount of vacuum matters - unless you can't get enough. Four 1/8 lines isn't going to give anywhere near the flow of a 3/8" (look at the area of four 1/8" circles vs one 3/8") but I suspect it'll work unless you have to stop with the car at full throttle and you empty the vacuum reservoir of the booster. It's worth trying.

Angry, feel free to correct me

Keith wrote: I don't think the amount of vacuum matters - unless you can't get enough. Four 1/8 lines isn't going to give anywhere near the flow of a 3/8" (look at the area of four 1/8" circles vs one 3/8") but I suspect it'll work unless you have to stop with the car at full throttle and you empty the vacuum reservoir of the booster. It's worth trying. Angry, feel free to correct me

keith is exactly right, sort of. funny thing is that on a track car they rarely make engine vacuum when you're not on the brakes, ie WOT WOT WOT BRAKE WOT WOT BRAKE. it comes down to the flow rate, how quickly can you evacuate the booster between applications.

FWIW, four 3/16" lines will give you exactly the same area as a single 3/8". is there a chance you can open up the individual ports to accomodate a 3/16" line?

this is what i got: http://weapon-r.com/english/images/962-111-101.jpg

so perhaps i can find some different fittings for the vac manifold?

FWIW, us FD RX7 peeples upgrade to the larger 1" master from the 929. The stock 93-95 RX7 is 15/16".

http://www.rx7.org/Robinette/mastercylinder929.htm

In reply to amg_rx7:

i LOL'd at the doc you linked. it is physically impossible for a larger-diameter master cylinder to decrease the pedal effort required to generate a particular line pressure, in and of itself. force = pressure times area, or stated another way, pressure = force divided by area. if the area went up, and the pressure stayed the same, then the force went up too.

you could get a vacume assist pump I found one in a 99 Saab 9-5 turbo car it is mostly plastic fairly light .

Stan

AngryCorvair wrote: In reply to amg_rx7: i LOL'd at the doc you linked. it is physically impossible for a larger-diameter master cylinder to *decrease* the pedal effort required to generate a particular line pressure, in and of itself. force = pressure times area, or stated another way, pressure = force divided by area. if the area went up, and the pressure stayed the same, then the force went up too.

You think you're so cool with all of your fancy math and knowledge, don't you?

AngryCorvair wrote: i'd say the ratio would be somewhere between (754/156) and (796/171), so for our purpose i'd call it 5:1.

Wow. I'm seriously going to rethink ditching the booster on my Rabbit to save a few pounds. Last non-assist car I had was a Bug. Yeah.