Staring at a lot of drum brake pictures & diagrams, noting there are very minor variations for the most part from 7" to 10" diameters. Still need to make some measurements. And then I get hit with the information that the '60s muscle cars (and maybe most of the Detroit iron) have a shorter friction surface on trailing shoes than on their leading shoes. Maybe it's just a '60s thing? Some were, some weren't. Problem with twin leading shoes is they sometimes grab worse than a leading-trailing shoe brake.
In the BrakeTorque calculation, the mean shoe angle (Am) is the most sensitive parameter while simultaneously being the angle we end up guessing due to a total absence of data. If I understand it correctly, this is how much of the shoe lining does NOT contact the brake drum during the life of the lining. It might be 45 deg shortly after bedding the brakes and then decrease to the shoe heel angle (A1) for the last portion of the brake shoe's life. Unfortunately, BrakeTorque really takes off as that angle goes below 30 deg, so I'm inclined to recommend 30 deg as the angle to use. In other research, the British cars have a lot of consistency/interchangeability across models since they typically used brakes from the same few manufacturers. Interchangeable parts make the spreadsheet a bit easier to design.
Looks to me, Emery, that you are about to become an absolute drum brakes expert. But will we ever get an answer about how harsh the brakes fade actually has been. How low they could get it to be ? Supposedly 300SLR had best ever drum brakes, and they still needed an air brake. Although they were mounted inboard, so... Brakes fade, engine braking - mysteries of the universe, harder to crack than Pyramids of Giza", "Stonehenge", "Women" and "Physics simracers thinks are good".
A question guys. If I copy paste the brakes parameteres of a car in another car, would this be sufficient to make the second car behave like the donor car in braking? Of course tires specs, car mass and also drag have a role, but beside these? Do I have to adjust other stuff? [edit] I make an example to make it clear. In the workshop there is a Ruf Yellobird with very weak brakes. Say that I copy paste the Corvette ZR1 or Honda NSX brake data in the Ruf, to improve its performance. Would be enough?
This is a wild offtopic, man. If you ask about how car behaves, and not just about performance of deceleration, then answer is - No. Everything in a car works together. You will have to copy whole physics lol. Having a car that is going to brake efficiently and be well balanced at the time of turning in is important to have. Speaking of the older 911designs, and the Yellowbird that still was very much an original 911 - the liftoff oversteer tendency was an important detail of its dynamics, so you might as well try to boost engine braking, but not too much. In attempt of dragging this to drum brakes. For example I have car (x) with drum brakes already adjusted to have braking torques and temperatures management and response which I assume judging by available evidence and common sense being correct. I can theoretically just transfer the parameters to cars (y,z). But cars y and z achieves absolutely different top speeds, and have very different masses. Aerodynamics are very different. Engines are very different. Then I look at available information if cars y and z were known to have good brakes, I look at their cutaway pictures and check how big drums were, were they placed somehwere where they could have been well exposed to cool air flow. Then I might just boost those brakes parameters to make the car brake as well as car (x) does, despite cars y and z being 200+ kg heavier, and arriving at most braking zones at higher speeds too. Then I check if a car is red or yellow and has horses painted somewhere, then I know that it has to be superior in every way (just joking).
My spreadsheet is coming along slowly as the scope has expanded more than I hoped. Still researching to reduce the guesswork (the art of drum brakes) and motivating myself to finish it. The self-actualization (self-energizing) effect of the leading shoe is a curve depending on the lining coefficient of friction. There's a nice chart in Rudolf Limpert's "Brake Design and Safety", third edition, on page 28. Unfortunately, ISI/S397 designed around disc brakes which are fairly linear, so rF & rF2 do not have the parameters to account for this effect. Consequently, we must use a crude approximation via a simple multiplier when it comes to calculating brake torque and it is called the brake factor. Fortunately that simple multiplier was also the historical answer for brake factor! Here is a table for brake factors according to the kind of drum brake as derived from the February 1954 Road & Track article, pg 38-39: Leading shoe-trailing shoe with pivot: 1 Leading shoe-trailing shoe sliding (maybe applies to "center pivot" used by Mercedes and Ferrari?): 2 Twin leading shoe: 4 Bendix leading shoe-trailing shoe (aka duo-servo): 5 An advantage of the simple multiplier is by using Limpert's chart, we can estimate the lining coefficient of friction in use in the '50s. I see a Cf range of 0.30-0.45, with the softer street linings at the lower end and the harder race linings towards the upper end. Unfortunately I still don't have solid temperature ranges for the linings.
Servo effect is indeed very interesting, for a long time I did not even know about it at all. I think we can worry not about rF2 lacking parameters to have it working. Probably even if it was possible to have it working, most people choosing these cars would still demand to reduce the effect, or even not use it. Although we would have joy to experience it.
Aha! That short shoe and long shoe pairing identifies them as duo-servo brake shoes. Bendix owned the patent and GM was the first corporation to use them in mass produced cars in the '30s and they gradually spread through Detroit cars. As examples, the first Corvettes and Thunderbirds both used duo-servo drum brakes. [Side note is that Bendix and Lockheed were the same corporation and they just sold different lines of products. USA tried unsuccessfully to break up the Bendix monopoly in 1948.] Here's a good explanation of how duo-servo brakes work:
Then there's the slow realization that since brake factor is dependent on both the kind of brake and the coefficient of friction, then the spreadsheet needs a different BrakeResponseCurve for each of the kinds of drum brakes because the coefficient of friction changes as the temperature moves out of the optimum zone. We can safely ignore the cold end of the BrakeResponseCurve for drum brakes, but on the hot end we should see the brakes fade sooner than happens with disc brakes (brake factor reduces as friction coefficient reduces). Remember that BrakeResponseCurve is independent of the thermal capacity of the brake drums/discs. This is the biggest reason I said earlier that ISI designed the system around disc brakes because though the brake factor still changes with the friction coefficient, the rate of change is so little that it can safely be assumed to be 1. If the system were designed with all brakes in mind, then there would be a brake factor curve for each of the different types of brakes and we wouldn't need to tailor the BrakeResponseCurve. In other reading, I found it interesting that a 1922 Aston Martin was able to stop from 60 mph in 120 ft. This is not much different from the typical sedan in the '70s, though I'm pretty confident that the '70s car's brakes were less likely to fade. The Aston Martin had mechanical brakes, with a hand lever operating on all 4 wheels and a foot pedal operating only on the front wheels!
I see no reason for ISI to design the system to include drum brakes, they're very niche, they didn't include preselector gearboxes either
Working now on the BrakeHeating and BrakeCooling calculations. Think I've got a handle on what's going on in the physics spreadsheet for BrakeHeating, but the BrakeCooling calculation is more difficult to understand. The BrakeCooling calculation relies on emissivity and that seems okay for iron/steel drums. Unfortunately when it comes to Al-Fin drums, it seems aluminum and magnesium, generally speaking, have low emissivity despite (or because?) having a low specific heat. But anodized aluminum has a high emissivity. I don't think the Al-Fin cast aluminum drums were anodized. The Lotus elektron drums seem to be a machined finish. To further complicate things, emissivity often increases as temperature increases. So my current mental picture is the Al-Fin style of drums willingly absorb heat from the steel/iron liner via conduction, but then are reluctant to give up the heat to the air? Something doesn't seem right about that as we use aluminum for heat sinks in electronics... help!
Oh yeah, approaching the good part. At the moment maximum I can do is a 10seconds googleing, which isn't useful or impressive at all. Google says tho that: "Thermal Conductivity Thermal conductivity is about how well a metal can maintain and transfer heat. While steel has higher heat resistance, aluminium conducts heat better. In fact, aluminium dissipates heat up to 15 times faster than stainless steel."
After playing with the numbers, emissivity is less critical than I feared it would be. I'm making progress with both BrakeHeating and BrakeCooling calculations, though it will take at least another week of off & on tinkering before they're done. There is more hand-waving magic in this section of the physics spreadsheet calculations than we'd all desire, so the best we can hope for is being consistent when working on different cars. Best of all possible worlds would be having some brake drum temperature charts from period cars to correlate with. Third best would be stopping distance charts (vintage road test charts from a slow 30 mph vs pedal pressure exist, but they don't specify what brake linings and tires were used and there are precious few charts of vintage lining coefficient of friction vs temperature available).
I never thought I'd say that a spreadsheet could have spaghetti code, but when it comes to the BrakeCooling & BrakeDuctCooling cells of the physics spreadsheet, that's exactly what comes to mind. Lots of jumping around between cells rather than an orderly sequential list of calculations.
You don't have much experience of spreadsheets then They are a form of code and any code will deteriorate into spaghetti unless discipline is maintained, analagous to the second law of thermodynamics.
LOL. I started with Supercalc on an Osborne 1 while working a summer job (*) back in 1981. Yeah, the problem is trying to understand somebody else's ideas and I'm not helping the spaghetti code much while trying to replicate the functionality. Another pass will definitely occur before I release it into the wild! (*) To namedrop, the friend that worked for the same engineer and helped me get the job that summer was future games inventor Richard Garfield.
Best I could do during January was open the spreadsheets, stare, and go do something distracting. Back on it today and gaining understanding... got a handle on the static cooling, which leaves the dynamic cooling section. Dynamic cooling includes air volume from the air intake area, air mass flow, and two numbers pulled from a hat (flow efficiency and cooling efficiency). I think the air intake area is of a cooling duct, so how to come up with a number if there is no duct? Once I get through this section, that settles the case for single metal brake drums. Then I have to blaze new ground to solve for the bi-metallic Alfin style of brake drum, where there's an iron/steel liner cast inside an aluminum or electron (magnesium alloy) heat sink.
I've mentioned brake factor regarding drum brakes earlier in this thread. Finally got around to scanning the complete page including my pencil marks. You can view it at https://drive.google.com/file/d/10vHIX5YNz4dickLoIw4u7EefjcproV6N/view?usp=sharing
I remember seeing one YT video where a specialist was explaing how much more effective drum brakes are comparing to disc brakes when effectiveness is based on system pressure. A lot more pressure is needed for discs. And then for drum brakes the servo effect makes it probably even too effective. Initially.
