Rotating Mass – Marketing Fallacy?

[Larry Hayashigawa]

Ok here it is. This calculation gives one an insight as to what is predominate in affecting the acceleration of the kart.

I calculated two models of weight and inertia.

The 1st model assumed a mass/weight of a 350 lbs kart. The 2nd model assumed that the entire 350 lbs of the kart were put on a theoretical ring that fit on the outside of the tire and no mass for the kart. Af first guess one would think wow a 350 lbs "tire" would certainly acceleration slower than a 350 lbs kart but these two configurations accelerate the same.

Here are the calcs:



EngTorq = 48 in-lbs (KT 100 Torque of 4 ft-lbs)
Gear ratio = 7.55

Model 1
Linear Acceleration of 350 lbs kart
Assume no rotational inertia only mass/weight of kart
Tire Rad = 5 in
weight = 350 lbs
TorqueWheel = 362.18 in-lbs
Force at track surface = 72.43 lbs
mass of kart = 0.905797101
Linear Accel = 79.96 in-sec^2
Linear Accler = 0.21 gs

Model 2
Linear Acceleration of 350 lbs "ring" placed at 350 lbs
Puts a ring of mass at tire circumference of 350 lbs
Kart has no mass

Inertia = 22.64 in-lbs-sec^2
radius = 5 in
mass = 0.905797101 lbm
Force at Tire/Track = 72 in-lbs
Linear Accel = 79.96 in sec^2 (had wrong dimensions, was in-lbs)
Linear Accel = 0.21 gs

[Chris Hill]

Todd,

If you reread what I wrote, I state nothing about an engine making more power. The entire purpose of this thread is how important is rotating mass for kart performance. I've answered the question with the true scaller of the equation. The issue is what drives the effective mass of the kart.

On F1 engines, I think the exotic materials is more for decreased mass for the sake of turning more rpm. The F1 guys are in a constant process of trying to get the engines to run a higher and higher engine speed and having the rotating/reciprocating parts live.

Driving down the rotating/reciprocating parts in an engine really show up at VERY high engine accelration rates. By very high, I mean in excess of 2000 rpm/sec during 1st gear of an A/SA NHRA stock eliminator car. The lighter parts really don't show up in 2nd gear, and hardly at all in high gear...

[Bob Mosso]

While watching TV last night I derived the equations necessary to quantify the performance benefit of a clutch with low rotational inertia.

Let’s start by calculating the rotational inertia of my daughter’s L&T mini dry clutch:
Iminidry = 0.5*m*r^2
Mass of the clutch = 0.542 kg (minus the starter nut and key)
Largest diameter = 3.49 inches, radius = 0.044323 meters
Iminidry = 0.000532387 kg m^2

I don’t have a multi disc wet clutch to measure, let’s assume:
Mass of the wet clutch = 1.0 kg
Largest diameter of the wet clutch = 4.0 inches, radius = 0.0508 meters
Imultiwet = 0.00129032 kg m^2

One could claim the mini dry clutch is 2.42 times better than the wet clutch. Let’s quantify this by estimating the difference in lap times directly associated with the different clutch.

Constants:
Deltarpm = rpm range that the kart is accelerated, i.e. from 10k to 14k = 4000 rpm
Teethengine = # of teeth on the engine sprocket = 11
Teethaxle = # of teeth on the axle sprocket = 87
M = total mass of the kart = 133.8 kg
Tiredia = diameter of the rear tire = 11 inches = 0.2794 meters
Tengine = constant torque output of the engine (greatly simplifies the calculations) = 9.0 newton meters

Calculated Values:
T = the time needed to accelerate Deltarpm
Tkart = the amount of Tengine used to accelerate the kart’s mass
Tclutch = the amount of Tengine used to increase the clutch’s angular velocity

Linear Motion:
T = Pi*M*Deltarpm*Tiredia^2*Teethengine^2/(120*Tkart*Teethaxle^2) (equation #1)

Rotational Motion:
T = Pi*Iclutch*Deltarpm/(30*Tclutch) (equation #2)

By our definition of the variables we also know:
Tengine = Tkart + Tclutch (equation #3)

We are assuming no clutch slip or tire spin, the amount of time to spin up the clutch will be equal to the amount of time to accelerate the kart, so the right side of equation #1 = the right side of equation #2. If we solve for Tclutch and simplify:
Tclutch = 4*Iclutch*Tkart*Teethaxle^2/(M*Tiredia^2*Teethengine^2) (equation #4)

We now have two equations (#3 and #4) and two unknowns (Tclutch and Tkart). Solving equation #3 for Tclutch and setting it equal to equation #4, then solving for Tkart and simplifying:
Tkart = M*Tengine*Tiredia^2*Teethengine^2/(4*Iclutch*Teethaxle^2+M*Tiredia^2*Teethengine^2) (equation #5)

Now substitute equation #5 into equation #1 for Tkart, equation #1 simplifies to:
T = Pi*Deltarpm(4*Iclutch*Teethaxle^2+M*Tiredia^2*Teethengine^2)/(120*Tengine*Teethaxle^2) (equation #6)

Plug in the numbers for the L&T mini dry:
Tminidry = 1.96764

Plug in the numbers for the multi disc wet clutch:
Tmultiwet = 2.00305

Summary and Conclusions:
Each time you accelerate from 10k to 14k rpm the L&T mini dry clutch will be approx 0.03541 seconds faster than a multi disc wet clutch. If a typical track has you accelerating 10 times per lap, the lighter clutch will result in a 0.3541 reduction in lap times. If you consider two karts:

Kart #1 Kart #2
Clutch mini dry multi wet
Chain #219 #35
Brake disc 3mm vented cast iron
Wheels Mag Aluminum
Total Weight 295# 295#

I would estimate kart #1 would be 1.5 seconds faster per lap for sprint karting.

Who wants to check my algebra?

Regards,
Bob Mosso

[Scott McFadden]

[quote="Larry Hayashigawa"] Af first guess one would think wow a 350 lbs "tire" would certainly acceleration slower than a 350 lbs kart but these two configurations accelerate the same.


Thank You
_________________
Scott

[Chris Parks]

[Scott McFadden]

I mentioned this earlier but the one critical element regarding the F1 car is that the engine rotating component axes are in-line, as opposed to a kart where the axes are all perpendicular to the direction the car travels. This literally does change everything.
_________________
Scott

[Christopher Ragan]

I just read through this entire thread.
Ever eat too much ICE CREAM?
Man what a headache.

[Bob Mosso]

[Tim Doll]

Scott

You better tell all those brilliant British race car engineers that they've been doing it all wrong all this time. According to your theory, if they make the engine transverse they can stop worrying about the rotational inertia of the engine......

Tim
_________________
Standard disclaimer - I'm FREE - No longer affiliated with any organization, I can say whatever I darn well please!.

Everett, Washington

[joseph hollinger]

This has got to be one of the truly classic forum threads. If it goes on
any longer, I vote we rename it the "McFadden" project You go
Scott, you really are the pit bull of EKN

[joseph hollinger]

[Rodney Ebersole]

Fun reading, Where are these kart tracks with out corners? Most my accelleration problems are when the tires aren't pointed straight.
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Rodney Ebersole

[Scott McFadden]

I don't believe there has been an F1 car with a transverse mounted engine at any time in recent memory.

The benefits of mounting V10s "lengthwise" as part of the chassis far out way the negatives of rotational losses.

(My) “misunderstanding of physics” well isn’t this special.

I may not have an in-depth knowledge of physics but I am able debate an issue without attempting to belittle, or impose my opinions and beliefs on others (except for one attempt at humour that upset the little E fan, and by the way there are british engineers involved in nascar, ouch).

I have made a legitimate effort to explain my understanding of some fairly straightforward laws as they apply to the issue, and I’ve tried to do it in terms that can be understood instead of long incomprehensible formulae that, while they may be correct, mean nothing to the average guy so are of limited value to me.

The argument that has been most prevalent against mine in this thread is apparently contained in a high school text to which I was blissfully unaware of until now. The example, in layman’s terms, basically assures that if one applies two completely different forces to two identical objects, the objects will have different types of motion. Of course I completely agree with the example. The trouble is, in the context of the original premise and original assumptions (remember constant force) the example is irrelevant to the argument so proves or disproves nothing.

After being beat-up here for a couple of days, it was certainly a relief to hear from a couple of people who are also prepared to challenge the common beliefs. I have much more respect for these individuals, whether they are right or wrong, than for anyone who attempts to “win” by belittling his opponent in the debate, or simply believes that because an idea is widely accepted, it must be right.
_________________
Scott

[Larry Hayashigawa]

OK, this whole topic was bothering me and earlier I posted some rough calcs and rounded some numbers off to illustrate that rotating inertia is a pretty small effect. To get more accurate, I dusted off an old program (TK Solver) and worked in both the rotating inertia effect and kart weight effect on acceleration. I put a sample page of the program as a graphic, hope it works.

As pointed out by in an earlier post; Yes, you effectively pay a double penalty with rotating inertia because it has to be linearly accelerated and rotationally accelerated but the rotational penalty is small.

Sample outputs:

1) Kart wgt = 330, Rotating weight = 20 lbs at 4" radius
Acceler = .201916 gs
2) Kart wgt = 335, rotating weight = 15 lbs at 4" radius
Acceler = .20069 g

Difference is about .6% in acceleration and this assumes that one could take out 5 lbs on a 4" radius, I've estimate that brake disc have effective mass radius of 3" or less plus I'd like to see a disc brake that could be made 5 lbs lighter. Even after all that you get a net gain in acceleration of .6%.

ENGINE ROTATING MASS
Rotating mass on the engine makes a difference but only when the clutch not engaged. Once the clutch engages the inertia of the rotating parts and the mass of the kart swamp out any engine related inertia. Inertia of the engine parts and clutch parts makes a difference because the engine can get to its engage RPM quicker.

[joseph hollinger]

.pdf available at http://home.earthlink.net/~joehollinger/cylinder.pdf