Lotus Elan

Simulation software for the Elan

PostPost by: msd1107 » Sat Oct 20, 2007 10:45 pm

Elementary simulation software for the Lotus Elan.

This whole thing started out quite innocently. Chatting with another Elan owner brought up the question as to the car?s possible top speed (with the tires and differentials available, an empty question). Well, a little work later brought a work sheet in which various vehicle parameters could be entered, and an estimate of the horsepower for a certain speed required was output. This is in worksheet ?Aerodynamic Drag?.

There is another spreadsheet in distribution that allows the user to calculate so-called optimum gearbox ratios (you can ask for a copy of this spreadsheet, it is too large to post). In any case, a debate developed about the optimum staging of gearbox ratios. So the suggestion was made that the aerodynamic drag work sheet be expanded to calculate acceleration times and thus allow ratio design to be optimized for minimum acceleration time.

Well, a little later, and various factors that affect acceleration were included, and a bunch of results tables and graphs generated that allow the obsessive and compulsive of us to determine the effect of various changes, even if they can hardly be discerned in real life.

So you can see the effects of different torque curves (low RPM torque vs high RPM power). See the effects of short shifting for different torque curves. See whether it is more beneficial for performance to increase the horsepower by 10% or decrease the weight and aerodynamic drag by 10%. And bunches of other things.

Posts in this forum have asked questions that can be answered by this spreadsheet, like what speed will my Elan do at X RPM, using Y differential ratio, Z tire size? What effect on performance will lightening the flywheel have? Even, in a tongue in cheek moment, what effect does the front bumper trim strip have on performance?

For most of us with daily drivers, these questions are of mainly academic interest. But if you are restoring your car from scratch, knowing the effects of some possible modifications can guide you in your restoration, whether you want an authentic appearance or are willing to make modifications. The Elan is a complex system, with a large number of sub-optimal systems dictated by the knowledge or economics of the day. One change may not have much of an effect, but identify and implement a second change, a third change, and there is the possibility of producing an Elan substantially improved over the original while using Chapman?s original design genius.

In any case, this is rather simple software, not that rigorously tested, that does not rise to the level available to F1 teams. But it has sort of opened my eyes about how different things affect performance. I hope that it improves your understanding also.

The spreadsheet is 1.8MB, so can't be uploaded in its original form. The spreadsheet is ZIPped. But LotusElan.net does not accept .ZIP files, so the file is renamed with a .XLS extension. After you download it, rename the file back to .ZIP, and extract the spreadsheet.

Be sure to tell me about invalid results, incorrect formulas, questionable assumptions, etc that always afflict the programmer. And also send me requests for enhancements etc.

Also, please send me other dynamometer curves, whether charts or tables. I will include them in the spreadsheet and post the updates.

And I am looking for camshaft lift curves, again either charts of tables.

If you modify the spreadsheet, please send me a copy.

Have fun.

David
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20070526zDragSpeed.xls
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PostPost by: John Larkin » Tue Oct 23, 2007 11:53 am

Dear David,

I cannot open your file. It seems to be corrupted.

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PostPost by: garyeanderson » Tue Oct 23, 2007 12:48 pm

msd1107 wrote:Elementary simulation software for the Lotus Elan.

The spreadsheet is 1.8MB, so can't be uploaded in its original form. The spreadsheet is ZIPped. But LotusElan.net does not accept .ZIP files, so the file is renamed with a .XLS extension. After you download it, rename the file back to .ZIP, and extract the spreadsheet.

David
1968 36/7988


Hi John

did you see this part about renaming the file?

Gary
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PostPost by: John Larkin » Tue Oct 23, 2007 1:15 pm

Thanks Gary --- that worked!

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PostPost by: ozone.breath » Sun Nov 04, 2007 6:33 am

David,
Unless I misunderstand how your sheet works, the entries for brake and wheel weight, etc, in the acceleration tab, are rotational inertia entries.

If these entries are indeed intended to be rotational inertia, then why are they a function of speed?

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PostPost by: msd1107 » Sun Nov 04, 2007 7:53 am

Erik,

The engine (flywheel), drive shaft, and tire/wheel/brake rotational inertia are all functions of speed.

For instance, 165-13 tires at 120 mph are rotating at 1774 rpm. The tire/wheel combination each is over 30 lbs. So at slow speeds, they are rotating slowly, and do not have much rotational inertia. But the effect builds up, as you can see. Just image the rotational inertia of large, heavy 335/45-20 wheel/tires, where the weight of an individual wheel/tire probably exceeds 50 lbs, especially at the higher speeds that these more powerful vehicles can attain.

The driveshaft rotates as a function of the speed with the effect of the differential ratio included. The driveshaft is not too heavy, so its effect is not too large. But the Honda S2000 apparently has a carbon fiber option to shave that last little bit.

The additional engine rotational inertia is a function of the speed, modified by the differential ratio and by the gearbox ratio. You can see this effect in the tables in rows 153-159 and 169-175. Increasing the engine rotating weight has an increasing influence on acceleration until at a certain level it actually forces a shift to a higher gear before the power peak for optimum acceleration.

Hope this helps.

David
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PostPost by: ozone.breath » Tue Nov 13, 2007 4:20 am

David,
Sorry, but rotational inertia, AKA moment of inertia, is definitely not a function of speed. Moment of inertia is defined by Newton's second law for rotation,
Torque = Moment of Inertia * Angular Accelertion.

Moment of Inertia does not vary with angular velocity.

I believe you may be thinking about Angular Momentum, which is described by the product of an object's moment of inertia and its angular velocity.

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PostPost by: msd1107 » Tue Nov 13, 2007 8:57 am

Erik,

Interesting commentary.

Both the vehicles linear inertia and its rotational inertia are a function of the vehicle speed.

For the linear inertia, we see this effect most ofen in particle accelerators, where as the particle velocity approaches the speed of light, its effective mass increases, until effectively the particle becomes so massive it cannot be accelerated as its speed approaches the speed of light.

At Lotus speeds, the vehicle mass can be treated as a constant.

Rotational inertia, on the other hand, varies as the square of the angular velocity. So the rotational inertia starts at zero and increases at the square of the angular velocity, which is the vehicle speed modified by the wheel size, the differential ratio, or the transmission ratio, depending on what effect is being calculated.

So the rotational moment of inertia may not vary according to the vehicle speed, but the rotational inertia does change according to the square of the angular velocity which is calculated from the vehicles speed and the wheel diameter, the differential ratio, and the gearbox ratio, depending in where the effect is being measured.

Textbooks and various web sites give formulas for this. One site is:

http://en.wikipedia.org/wiki/Moment_of_inertia

But there are others with the same formulas.

Hope this helps.

David
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PostPost by: msd1107 » Tue Nov 13, 2007 8:20 pm

Thinking about this some more ...

Here is another web site that gives the correspondence between linear and rotational inertia.

http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html

Linear moment of inertia is mass (m), the weight of the object. Rotational moment of inertia is I, which depends on the mass of the object and its shape.

Linear momentum is mv, mass times velocity. Angular momentum is Iw, rotational moment of inertia times angular velocity ( w should be the Greek symbol that sort of looks like w and is angular velocity.)

The spreadsheet computes I for each of the rotating components, using simplifying assumtions about the geometry. So the tire gets its computation, the wheel gets its computation, as do the brakes, driveshaft and flywheel. The spreadsheet is unlocked, so anybody can stare at the formulas. But if anybody has any questions, email me and I will try to answer.

Thankfully, the mathematics are not nearly as involved as what goes into MP3 files or HDTV video compression!

Hope this helps.

David
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PostPost by: rgh0 » Wed Nov 14, 2007 9:09 am

David

You are confusing the terms "inertia" with "momentum". Linear and rotational inertia are a property of the item under consideration and a constant at below relativisitic velocities. Momentum is a function of inertia times velocity and increases with velocity be that angular velocity and angular momentum or linear velocity and linear momentum.

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PostPost by: msd1107 » Wed Nov 14, 2007 6:45 pm

Rohan,

Right you are! Give me a F for the ability to exposit.

The post yesterday and the link in it show this. I am red faced about the confusion and apologize to all.

David
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PostPost by: ozone.breath » Thu Nov 15, 2007 1:43 am

David,
Whew! I'm glad that you have now gotten the difference between inertia and momentum sorted out.

OK, so the next thing is (and I haven't gone back to look at your spreadsheet again, so I am depending on my unreliable memory and your forum comments, regarding this item) is there something in your spreadsheet that is squared in angular velocity? If so, then it probably is proportional to rotational kinetic energy, not momentum or inertia.

Despite your confusion over inertia / momentum terminology, I think that what you INTENDED to describe in those fields of your spreadsheet was angular momentum. If that is true, then there may still be a serious problem if those entries are actually squared in angular velocity.

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