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Re: Building Gold Stars using Simulation Software [Re: Gordo in Comox] #778559 07/13/19 3:43 pm
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Originally Posted by Gordo in Comox
Did the dealers make standard Scramblers into Catalinas by sticking on a decal and using the name in the adverts even before the factory recognized the unique model?
Gordo,

Ian Jackson found the DB34 bikes that left the factory starting in 1956 are in the despatch records as 'Catalina' so it was a genuine factory model, not "dealer-manufactured" with a decal. However, what I believe is currently unknown information is at what point the 'S' stamp was added below the engine number, and if it only applied to Catalinas or was also on "ordinary" Scrambles models available to the rest of the world.

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Re: Building Gold Stars using Simulation Software [Re: Magnetoman] #778752 07/15/19 10:38 pm
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The engine simulation project made a huge step forward today with the arrival of a Catalina head on loan from NYBSAGUY. The photograph shows it sitting on a 500 cc cylinder that is bolted to the top of my flow bench.

Scrambles models used 65-2446 cams for both the inlet and exhaust, having maximum lift 0.404". But, since the reason for doing these simulations in the first place is to be able to answer 'what-if' questions, I'll measure the inlet lift to 0.442" in case anyone ever feels the urge to install a Clubman cam in their Catalina but wonders what effect that might have.

I've started making the necessary valve opening fixture to bolt to the top of the head that will press the valves open in increments measured by a dial indicator. Maybe the fabrication will be more difficult than I expect, in which case I'll come to understand why the prices of such fixtures start at over $300, with many versions selling at more than double that.

Attached Files FlowBench_Catalina.jpg
Re: Building Gold Stars using Simulation Software [Re: Magnetoman] #778757 07/16/19 1:06 am
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And, as a quick PS..

Lest you think I prepped this head beautifully for MMan's experiments, full disclosure requires me to tell you that I sent it first to Phil Pearson, who breathed on it quite beautifully. So beautiful that I haven't been able to bring myself to assemble the engine. Just as well, as it turns out.

Now, let if flow, let it flow, let it flow...

Re: Building Gold Stars using Simulation Software [Re: Magnetoman] #778882 07/16/19 11:48 pm
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Originally Posted by Magnetoman
[

But, keep in mind I didn't buy this program to try to build an engine to win the IoM or set a land speed record. I bought it to try to accurately model the output of Gold Star engines as they left the factory 60 or so years ago in order to then run 'what-if' simulations with different cams, carburetors, etc. For this, the biggest limitation I can see thus far is the inability to enter something like the behavior of the Clubman's semi-reverse-cone megaphone. The program handles the effect of the length of a pipe, but the additional strength of the pulses due to the megaphone is an uncertainty. However, the Scrambles data with straight pipes allows me to gain confidence in the simulations.



The software I mentioned does have the options to define complex exhausts including reverse cone megaphones.

Going back to Blair, the top end commercial programmes and computer performance. i read a paper about ten years ago where the modelers were varying 3 parameters at a time. The output was a contour map in three dimensions. Run times were 24 hours plus.

When modelling exhaust systems for a twin project for a friend introducing a balance pipe between two exhaust pipes took the run times up to 5 hours compared to 30 mins for single pipes. The optimal system ended up looking like a BMW airhead exhaust system. Not a big surprise perhaps !

I imagine a good modern PC would do the job in a few minutes

Re: Building Gold Stars using Simulation Software [Re: Magnetoman] #778890 07/17/19 1:14 am
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Originally Posted by johnm
Going back to Blair, the top end commercial programmes and computer performance
It would be very easy for someone like me to get sucked down that rabbit hole (as if I'm not already down another rabbit hole, albeit one that -- I hope -- has a way out of it before too much longer).

Although it's unlikely I'll ever want to flow test an exhaust port, it didn't take all that much more time to make a "universal" Gold Star valve opening jig than it would have to make one for the intake only. However, the intake valve is at an angle of 33°45' and the exhaust is slightly different at 33° so I "optimized" the jig for the intake.

Despite what I wrote in the previous paragraph, the first photograph shows me milling the "riser" for the jig at an angle 33°. Actually, the angle of this piece isn't critical and the easiest way to make it was in the vise using 30°+2°+1° angle blocks. After fabricating the base and welding the riser pieces I then clamped it on an adjustable table set to ~33°45' to drill and tap the holes for the adjusting bolt and dial indicator. This placed the adjusting bolt precisely co-axial with the intake valve and the indicator precisely parallel with that axis. The slots in the base allow the jig to be dropped over either the intake or the exhaust studs, whose patterns are mirror images of each other.

The final images show two views of the jig as mounted to the head. Three features aren't apparent in the photographs. One is that, although the indicator hangs over the end of the tubing, there is a washer between the indicator and the jig to have its mounting point as close as possible to the lever arm of the adjusting screw. Because of this, even if the tubing bends under the load the indicator will be displaced by (approximately) the same amount as the adjusting screw. Another is I TIG-brazed silicon-bronze to the tip of the adjusting screw so a relatively soft material (Rockwell C hardness <2) is in contact with the end of the valve to avoid any possibility of abrasion. Finally, I Tig-brazed a nut to the underside of the arm because the tubing wall thickness only allowed for a couple of threads and they might not have supported the full force of the valve spring.

I had to end the day early because of other commitments, but I did do a quick check of the apparatus before I finished. Everything seems to be working well, so tomorrow I flow test.

Attached Files ValveOpener01.jpgValveOpener02.jpgValveOpener03.jpgValveOpener04.jpgValveOpener05.jpg
Re: Building Gold Stars using Simulation Software [Re: Magnetoman] #778957 07/17/19 6:06 pm
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Thanks to having NYBSAGUY's Catalina head on the flow bench I made significant progress with the Engine Analyzer software today. And the day isn't done yet. However, things always seem to become more complicated when you get into the details and this is no exception.

The software has separate entries for the flow of the carburetor and of the inlet tract, which perhaps suggests I shouldn't install the carburetor for the flow testing because the program wouldn't be able to distinguish between the fundamental restriction of the inlet port and that of the carburetor when calculating the efficiency. However, the SuperFlow manual says "it is strongly recommended" to install an inlet guide which they suggest should be "about one port width in thickness" (i.e. ~1.2") and "generously radiused on the inside all the way to the head."

In any case, since the purpose of this flow testing isn't so much to determine the absolute flow rate, but rather to determine the inlet port "Flow Efficiency," it's pretty clear that I'll need to make a radiused inlet guide to send the air smoothly on its way into the head. However, I couldn't wait to make that guide before running a test. That is, a test, test.

Making a long story short (because it will change), despite not yet having an inlet guide I ran the flow tests up to full lift for a 65-2446 inlet cam. As a reminder, the program gives the following efficiencies to use if flow data isn't available:

55% racing heads
57% good racing heads
60% very good racing heads
65% excellent racing heads

If flow data is available the program allows entry of up to 8 lifts, calculating the flow efficiency at each lift. What I found is for lifts of ~0.2" and less the program calculates values for the Catalina head of ~58%, but then decreases to ~54% at 0.3" and 48% at full lift of ~0.4". Although it remains to be seen, I suspect the inefficiency at high flow rates might be due to turbulence due to the lack of that radiused inlet guide that I'll now be fabricating.

Anyway, at this point my preliminary finding is a 60-year old Catalina head seems to be a "good racing head" even by 2019 standards.

Re: Building Gold Stars using Simulation Software [Re: Magnetoman] #779052 07/18/19 5:17 pm
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I had a short length of 4½"-dia Teflon rod that was perfect for making the tapered inlet. Since 3-angle valve jobs have been researched extensively for maximizing flow I decided I'd use those values. After boring the hole the same ID as the inlet to the port, I then cut 15°. 30° and 45° tapers. To avoid having the mounting studs project into the flow I carefully measured their lengths and then drilled to just those depths, relying on a tight slip fit over the studs to hold it in place. This mounting scheme worked very well as can be seen from the second and third photographs, with the Teflon pushed just slightly into the taper at the studs. With the tapered inlet in place, a quick measurement showed that near full lift the head flowed ~6% more than the bare head so having it does make a difference.

After entering the results into the program I then read the manual to find it bases its calculations only on the flow results at the value of lift corresponding to the ratio of lift to valve diameter = 1/4 (i.e. L/D=0.25), noting that once that point is reached the area of the inlet port rather than the area around the valve is what limits the flow. Since the inlet valve is 1.85" that's a lift of 0.46". This means all the time I spent measuring the flow at lower lifts was wasted, at least as far as the program is concerned, and I only needed to have measured the flow at a lift of 0.46" (I stopped at 0.404"). Oh well, live and learn. Actually, my "iterative" process is deliberate since by quickly running through the entire set of measurements and calculations I learn what I need to spend time on, and what requires less attention.

L/D explains why the program helpfully asks me if I've made a mistake with the valve diameter because it appears to be too large. Also, the lift of 0.46" for L/D=0.25 is close to the 0.442" lift of the Clubman cam (0.404" for the Catalina), which is consistent with the valves having been optimized for the Clubman engine and simply reused on the Catalina without further optimization for the smaller inlet tract and lower max. rpm (6500 vs. 7000).

Attached Files SuperFlow_Inlet01.jpgSuperFlow_Inlet02.jpgSuperflow_Inlet03.jpg
Re: Building Gold Stars using Simulation Software [Re: Magnetoman] #779092 07/19/19 1:10 am
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The problem with having data is it ties your hands. Unfortunately, now having good flow data on NYBSAGUY's Catalina head I'll have to spend more time with the program to get back to where I was before I had the data.

Originally Posted by Magnetoman
...bases its calculations only on the flow results at the value of lift corresponding to the ratio of lift to valve diameter = 1/4 (i.e. L/D=0.25),
The diameter of the Catalina's inlet valve is 1.85" so I measured the flow at values of the lift around 0.25x1.85"=0.462". Plugging these values into the program gave an inlet flow efficiency of only 47.8+/-0.2% at L/D=0.25. Given what I wrote before about "good, "very good," etc. racing heads, this seemed quite low. It falls between the flows of modern "as cast aftermarket heads" and "ported aftermarket heads."

For a while I thought I had done something wrong but, after carefully redoing the measurements, I found the attached table in the manual (yellow highlights added by me) indicating ~48% actually was very good for an engine designed in the mid-1950s. So, having this data, and since the data makes sense, my hands are tied.

I'm joking, of course, since the more data I have for the program, the fewer adjustable parameters (i.e. uncertainties) there will be. This only will make the final simulation that much more robust.

On the subject of additional data, I already have the air cleaner assembly off my Catalina waiting for its turn on the flow bench. But, Gordo and I only have one dyno curve for a "Scrambles" DBD, not a Catalina, so that's going to be a limitation until it's solved.

p.s. The SuperFlow manual gives a formula for the maximum power for a "well-tuned racing engine" that has "the maximum compression, the right cam, and a tuned exhaust system" that is calculated from the measured flow at maximum valve lift. Assuming my friend's Catalina had a Clubman cam installed (i.e. with greater lift than the Scrambles cam), higher compression piston, and a tuned exhaust rather than a straight pipe, this formula estimates it should produce 50.5 h.p. That's 1/3 more h.p. than a Catalina in stock configuration was measured to produce on the dyno so the estimate from the formula is too optimistic, but it does indicate my friend's Catalina head is in excellent condition.

Attached Files EngineAnalyzer_FlowEfficiencies.jpg
Last edited by Magnetoman; 07/19/19 6:02 pm. Reason: p.s.
Re: Building Gold Stars using Simulation Software [Re: Magnetoman] #779312 07/21/19 7:30 pm
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That damn NYBSAGUY just cost me $40. If he hadn't loaned me his Catalina head to test I wouldn't know the inlet tract flow efficiency was so low (by 2019 standards), so I wouldn't now be facing the problem that the simulation runs into a wall at ~5500 rpm. I've checked for obvious, and non-obvious, mistakes (e.g. converting flow measured at one pressure to the figure needed by the program at
another pressure), but the h.p. rises nicely to ~5500 rpm and then turns over. So, I had no choice but to have the ~300 page manual printed. And, worse than that, I now have to carefully read it in the hopes of finding what is going wrong. Damn you NYBSAGUY!

Re: Building Gold Stars using Simulation Software [Re: Magnetoman] #779377 07/22/19 1:25 pm
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<<Damn you NYBSAGUY!>>

Ha! This is only the beginning. I'm going to cost you a whole lot more by the time this is over..

Re: Building Gold Stars using Simulation Software [Re: Magnetoman] #779445 07/23/19 1:50 am
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My wallet took a hit, but as a result I'm moving forward again.

The black lines are traces of the dyno curves so I don't have to make the simulation partially transparent to see them.

Attached Files DBD_Scrambles67xx_sim001.jpg
Re: Building Gold Stars using Simulation Software [Re: Magnetoman] #779451 07/23/19 5:19 am
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It's working then..


No generalisation is wholly true, not even this one.
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Re: Building Gold Stars using Simulation Software [Re: Kerry W] #779453 07/23/19 5:42 am
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Originally Posted by Kerry W
It's working then..
I'd say it's working very well indeed.

Re: Building Gold Stars using Simulation Software [Re: Magnetoman] #780273 08/01/19 4:58 pm
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Hi

I'm new to the forum and only quickly run through the simulation work you have carried out. As a Goldie racer of some years I've also taken a "modern" approach to engine development by purchasing a copy of the Vannik 4t programme. It is a somewhat more powerful programme using the development of Prof Blair. Not only has Cornelius been a great help but also his Beta tester.
What you will find as you progress in making small alterations is the outcome will not match the popular misconceptions. No1 being more flow=more power. Is your software able to show pressure wave in the form of a graph at all the tested rpm. This is invaluable. It highlights the truth of what makes the engine, and that is pressure differential.
Keep up the good work. With careful selection of standard bsa parts and exhaust/inlet dimensions a 20% increase in power with the 500 is easily found.

Re: Building Gold Stars using Simulation Software [Re: Magnetoman] #780278 08/01/19 5:39 pm
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Originally Posted by Elfin jnr
I've also taken a "modern" approach to engine development ... popular misconceptions. No1 being more flow=more power. Is your software able to show pressure wave in the form of a graph at all the tested rpm.
Thanks very much for your post. My goal is perhaps different than yours, in that I "only" want to determine the effects of substitution of various stock BSA components on otherwise-stock engines. I'm not trying to investigate the (more complicated) effects of modifying the inlet port, installing a smaller/larger exhaust valve, a second spark plug, etc. The questions I hope to answer are of the type, what would be the effect on the h.p. and torque vs. rpm of, say, installing a Clubman inlet cam in a Scrambler, or using an 8:1 piston instead of a 10:1?

My flow bench measurements aren't to increase h.p. but simply to characterize the flow of standard components. On this topic, don't tell NYBSAGUY who loaned me the Catalina head, but out of curiosity a week ago I ordered silicone casting rubber that I will use to make a mold of the inlet tract. If I'm unable to remove the slug of silicone from the tract I expect it might reduce the h.p. of his engine somewhat, which is why I don't want him to know I'll be doing this.

My simulation work has been on a temporary hold while I catch up on another project that, unfortunately, has actual milestones and deadlines. However, I hope to get back to it within a few more days. So many interesting things to do, so little time...

Re: Building Gold Stars using Simulation Software [Re: Magnetoman] #780296 08/01/19 8:52 pm
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Originally Posted by Elfin jnr
exhaust/inlet dimensions a 20% increase in power with the 500 is easily found.


Originally Posted by Magnetoman
[quote=Elfin jnr] effects of modifying the inlet port, installing a smaller/larger exhaust valve


First..MM i understand what you want.. BUT Elfin nr does not mean necessarily that dimensions (valve dia. and modifying ports) .. only length and diameter of both inlet (carb incl manifold etc) and exhaust pipe alone can have such an effect on power.. so race cam in clubman with specific inlet length and specific exhaust length, behaves different in a scrambler with same basic engine/volume and compression ratio same race cam but with other length carb (incl air filter)/ inlet tracks and exhaust length (and diam.)

I presume you know this, so I am very curious how the “end” and result list, will show up ;-)


Harold
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Re: Building Gold Stars using Simulation Software [Re: Magnetoman] #780329 08/02/19 3:44 am
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Evening, all..

I have not been following this thread, because I am way to busy on other stuff.

But I did send MMan my head, for experimentation purposes only. And now I hear he is going to create a silicon mould of my inlet. Well, I say.. I think you might have told me. But it begs the question, Which inlet?

Re: Building Gold Stars using Simulation Software [Re: Magnetoman] #780646 08/05/19 10:18 pm
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Motolab is correct in what he says. The exhaust fitted to the 350/500 is generic and made to fit the bike/frame, as is the carb. By simulating the engine with what mechanicals you have, you are now in the enviable position to read the pressure traces and design an induction and exhaust system to create the best case scenario. What I like to call equilibrium. Ie at the point of the inlet valve opening Inlet pressure needs to be greater than cylinder pressure. Like wise the exhaust pressure, at the manifold also needs to be below that of the Inlet. As the cylinder fills and pressure in there goes up, the inlet port pressure should follow as close and for as long as you can possibly get it before the Inlet valve closes. You will then see inlet port pressure "bounce" as the superposition wave goes back and forth. Lengthening the inlet will reduce the number of bounces. The fewer bounces the less that pressure point is eroded.
Get these timings and others not mentioned working in harmony and the benefit far greater than any flow bench test can ever possibly generate.

On the software side, I need the ability to convert cam profile results at the valve. This is due to using modified Rocker arms of various lengths. Does any of the software you have viewed given this kind of usability?

Re: Building Gold Stars using Simulation Software [Re: Elfin jnr] #780653 08/05/19 11:30 pm
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Originally Posted by Elfin jnr
using modified Rocker arms of various lengths. Does any of the software you have viewed given this kind of usability?
I don't remember what I found when I was looking at the various programs on the market, but ' Engine Analyzer Plus' by Performance Trends that I'm using allows ratios up to at least 1.8:1.

I've hit another roadblock thanks to Microsoft. It did some sort of major update to Windows 10 last week and as a result my home office computer no longer recognizes any printer (sadly, it's not a simple issue of reinstalling the printer). It also changed various settings for other programs (I'm still discovering new issues). My work-around for the printer is to transfer files to my laptop and print from it, but this is quite a headache. My laptop also got the same upgrade but is still able to print, although other settings were altered and at least one program I use now won't open and diagnostics says it's incompatible with Windows. Not being able to print the 'Engine Analyzer' results makes comparing the results of changes essentially impossible. Hope springs eternal that I'll get it working again before too much longer.

Re: Building Gold Stars using Simulation Software [Re: Magnetoman] #786642 10/09/19 2:38 pm
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Originally Posted by Magnetoman
... update to Windows 10 last week and as a result my home office computer no longer recognizes any printer ... Hope springs eternal that I'll get it working again before too much longer.
I wrote the above two months ago. For those interested in these simulations who might have given up hope since then, I think I now have a "permanent" fix to the printer problem. I got the computer to recognize the printer for a few weeks since I wrote the above, but another Windows update severed the connection again a month ago and since then I've only been able to print by transferring files to my laptop. Anyway, fingers crossed that this new fix is more robust than the last one so I can fire up the simulation effort again.

Re: Building Gold Stars using Simulation Software [Re: Magnetoman] #786645 10/09/19 3:32 pm
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I share your pain MM.

My business (a very large Engineering company) has recently upgraded everyones laptop to the latest business standard item and the OS to Windows 10. I can honestly say that it is the worst OS I have had the misfortune to have to suffer on a daily basis. This is not just my opinion but the universal opinion of everyone in my office.

I sincerely hope that your printer problems are the only issues that you experience. At least you can have a go at sorting it yourself rather than have to rely on an IT Hell Desk due to the fact that everything has been tamper proofed.

John

Re: Building Gold Stars using Simulation Software [Re: Magnetoman] #786649 10/09/19 4:25 pm
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My friends in architecture and design (including, I am sure, MM's architect daughter, though I haven't asked her) also share this pain. They are split between Macs and PCs, but the design work is largely done on PCs. And they are having a nightmare since the recent upgrades, both to the OS and to the various drafting, modeling and draughting apps that they use.

The lesson is, and perhaps this should be written as a scientific principle: Things don't always necessarily get better.

Re: Building Gold Stars using Simulation Software [Re: Magnetoman] #793212 12/17/19 6:33 pm
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Avoiding actual work by escaping to work on my trailer is winding down, so I've turned back to engine simulations as my principle outlet for avoidance.

Since I last worked on this I received one more dyno sheet, which broke the back of my notebook and I had to bring a second one into the operation. All the ZB-DB sheets are now in one book and I moved all the DBD to the second one. In both cases, I have each 'series' (e.g. ZB) and each configuration (e.g. Clubman) separate and with the sheets in increasing order of engine number to make it easier to spot differences or changes.

In moving the DBD sheets to the new notebook I noticed something I hadn't before (or, that I had, but since forgotten). All six of the Clubman DBD dyno data run from 5000 through 7000 rpm, and two of the three Scrambles DBD data run from 4000 through 6500 rpm. This makes sense in terms of the intended use of the machines. However, the third Scrambles sheet, which has the lowest engine number and further is a Catalina, runs from 5000 through 7000 rpm.

The pre-printed sheets only have 'Scrambles' and 'Clubman's' on them, with one of them crossed out as appropriate. This is also the case for the third "7000 rpm" Scrambles sheet which I know to be for a Catalina, although there is no mention of that on the sheet. One of the "6500 rpm" Scrambles sheets has a different format and lists the cams, which are 65-2446 for both the inlet and exhaust. This is what the BSA literature lists as correct for a Scrambles Gold Star. None of the Clubman's sheets lists the cams, but the literature gives 65-2442 inlet and 65-2446 for the exhaust of those machines. Different inlet cams, different rpm ranges.

OK, back to the "7000 rpm" Catalina. I only have the single sheet that I know is for a Catalina, but does the fact the data for it runs to 7000 rpm mean it was built with Clubman's cams? It happens that this bike is a fairly early Catalina (engine no. 43xx), tested in June 1959, so a further question is that even if the early ones came with Clubman's cams, did this practice continue for later ones?

The more information I gather, the more questions that are raised.

Re: Building Gold Stars using Simulation Software [Re: Magnetoman] #793236 12/17/19 10:43 pm
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Very interesting.

My Catalina is a 59, with engine #43**. But it came to me with different cams, the 65-2446 exhaust, the 65-2442 inlet.. Of course I don't know if that is how it was shipped. The BSAOC told me that my bike was shipped with 65-2446 cams, but I don't think they had actually looked at the dispatch records for that bike.

Re: Building Gold Stars using Simulation Software [Re: Magnetoman] #793249 12/18/19 12:58 am
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Originally Posted by NYBSAGUY
Very interesting.
My Catalina is a 59, with engine #43**. But it came to me with different cams, the 65-2446 exhaust, the 65-2442 inlet.. Of course I don't know if that is how it was shipped...
Very interesting, indeed. That Catalina dyno curve I referred to is the one from your bike. I'd forgotten what cams you said came with it but, in light of this, I think there's a very good chance it came from the factory with the cams that you now have, i.e. Clubman's cams. The person at the BSAOC who told you it was shipped with a pair of -2446 was (incorrectly) assuming that was the case because the dyno data was marked "Scrambles." This certainly isn't the first time the configuration of a U.S.-only bike befuddled a Brit.

OK, we've established with pretty high certainty that your #43xx 1959 Catalina came from the factory with Clubman's cams. Irrespective of the intended configuration all Gold Star engines were stamped sequentially. The first Catalina in a CB32C frame was engine #377x in frame -101 and, without checking with you, I know from the date n the dyno sheet that your frame would have been ~-300, i.e. it was within roughly the first 200 Catalinas with CB32C frames that were made. Questions this raises include:

-- Were any or all of the pre-CB32C Catalinas shipped with Clubman's cams?
-- Were all of the initial ~200 (or more) 1959 CB32C Catalinas shipped with Clubman's cams?
-- If Clubman's cams were used for a period, at what point (if ever) did they stop being used?

The rabbit hole continues to get deeper.

For those who are interested in what difference it might make to put Clubman's cams in a Catalina head, thanks to my age-appropriate TI59 programmable calculator, we now have the experimental, not simulated, answer:

[Linked Image]

The black curves are from the sheet that explicitly lists the -2446 pair of cams and the green overlay is the h.p. curve from the 1959 Catalina whose dyno curve covers the 5000-7000 rpm range normally seen on Clubmans machines. However, it's not so simple, because the black Scrambles curve comes from an engine 2300 higher in number and progress was made in increasing the h.p. throughout the time of production. That is, a Catalina early in the production cycle with Clubmans cams produced more h.p. than one made much later in the production cycle with Scrambles cams.

While you're thinking about the above graph, how about a, ahem, head-to-head comparison of an actual Clubman and that same early Catalina? The next graph shows just such a comparison for a Clubman engine only 228 higher in number than that early Catalina. I'll leave you to ponder this without making further comment (because I don't know what comment to make)

[Linked Image]

Last edited by Magnetoman; 12/18/19 2:55 am. Reason: added graph and explanation
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