ESE's works engine tuner

[ApolloMotoMoto]

The student returns with another question

Can someone please check my math?



We did calculations for Flywheel Moment of Inertia.

I = (k)mr^2

Sub-divided each part, used the mass for that part, and the k constant that made sense for that part; k=1 for the rim, k=0.5 for the hub, etc.

Using pounds for mass and feet for radius, this is how we got to 266 ld ft^2 for the flywheel by itself.
Using the same units for the drop test, we ended up with 280 ld ft^2.

Okay, now I have a value for Inertia in the torque equation T=Ia

All bright eyed and bushy tailed, I calculated the angular acceleration of the flywheel for a test pull that was just conducted with a 212cc 4 stroke engine that should make 8.1ft ld ft of torque peak, and about 6.5 hp peak. (Honda Generator Engine Clone)

I dont have the recorded pull data to see the actual curve shape, but I know the start and end engine RPM's of the pull, I know the time of the pull in seconds, and I know the gear ratio between engine and flywheel shaft.

RPM range = 1000 Engine RPM to 5000 Engine RPM
Pull Time = 15 seconds
Gear Ratio = 6:1 (10t on engine crankshaft, 60t on flywheel, no transmission, no clutch)

Thus, averaged across the pull, the engine accelerated at a rate of 266.66 RPM's per second.
Using the 6:1 gear reduction, this means the flywheel accelerated at an average rate of 44.5 RPM's per second.

The software has a sampling frequency of 5 samples/second.

So, I decided to look at 0.2 second "steps" of time for the rate of angular acceleration (a). Using the average acceleration rate of the Flywheel I whitled down to:

44.5 RPM's per second = 0.74 RPS's per second = 0.148 RPS's per data point (per 0.2 seconds) = 0.93 angular velocity (w) per data point

So, if this is averaged across the whole run, each data point will have the same (w), and thus the same delta(w).
Same thing for time, every data point is 0.2 seconds "wide", so delta(t) will always be 0.2.

Finaly;

a = delta(w) / delta(t)
a = 0.93 / 0.2
a = 4.65


Now, armed with all of the mathematical powers needed to divine the measured engine power.... everything falls appart.

T=Ia
T=280 * 4.65
T=1302

1302 ft lds of Torque measured at the flywheel shaft?!?!?!
-okay, thats a little big, but thats flywheel shaft torque, so lets divide it by the 6:1 gear ratio to find out what the engine did....

1302 ft lds / 6 = 217 ft lds of "average" Engine Torque across the 15 second pull.

Thats a fever dream, not a measurement....


After considering my life decisions for a few hours, I think I stumbled into my problem:


I = (k)mr^2 only works with SI units.

The output of that formula when we use pounds and feet is absolute bunk for executing the T=Ia formula.

So, I redid the Moment of Inertia Calcuation using SI units.

I end up with 11.8 kg m^2 after converting the weight of the flywheel in lds to kgs (110ld flywheel), and converting the radius to meters (2ft radius flywheel).
-lets try this one more time:

T=Ia
T=11.8 * 4.65
T=54.87

54.87 Nm of Torque measured at the Flywheel shaft, that sounds more like reality.
54.87 Nm lds / 6 = 9.15 Nm of "average" Engine Torque across the 15 second pull.
9.15 Nm converts to 6.75 ft lds.

6.75 "average" ft lds across a pull from 1000 - 5000, using a 4 stroke engine that makes ~8.1 ft lds of peak torque at 2,500 RPM?
-considering this 6.75 ft lds is "uncorrected power", and the ~8.1 ft lds number is the manufacturer advertised, SAE corrected output.

That sounds like a real measurement.

Now, lets check HP using flywheel RPM like Neels just advised.

To do this, I took the 54.87 Nm of flywheel shaft torque and converted it to ft lds;
54.87Nm converts to 40.47 ft lds

Using 40.47 for torque and flywheel RPM for RPM, I calculated HP at 1000 Engine RPM (166 flywheel rpm) and 5000 Engine RPM (833 flywheel rpm).

HP = T * (RPM / 5252)

If the Torque curve is averaged to the "flat line" of 6.75 ft lds of torque at every RPM step like I have done;

HP at 1000 RPM = 1.3 HP
HP at 5000 RPM = 6.4 HP

That is "in the ballpark" as they say.

Final sanity check;

The pull did not go to 5252 RPM, but if I keep extending the averaged 6.75 ft lds of torque out to 5252;

HP at 5252 RPM = 6.75
Torque at 5252 RPM = 6.75


HP and Torque "cross over" at 5252 RPM's!

Woohoo!


Can someone please check my math and give me a positive confirmation that I = (k)mr^2 only works with SI units for the purpose of using in the formula T=Ia?

[wobbly]

Math apart - do not be focused on the Hp/Torque graphs " crossing " at 5252 - that is a completely irrelevant but automatic metric.
Set the scales such that they are the easyest to read and interpret , having a wider scale on Torque can reveal subtleties not seen when the Y scale is compressed
to include Nm that are not even used on track and thus are not needed when dyno testing.

[ApolloMotoMoto]

Can someone please check my math and give me a positive confirmation that I = (k)mr^2 only works with SI units for the purpose of using in the formula T=Ia?

I figured it out!

It doesnt work with pounds because the pound is not a unit of mass (m) its a unit of weight.

The Imperia SI unit for mass is the slug.

This is the first time I have ever heard of a slug.

1 Slug = 32.17 pounds

Thus;

lds/32.17 = slugs

If you use slugs per square feet for the I in: T=Ia;

The resulting T will be in pound feets.

If you use kilograms per square meter for the I in : T=Ia

The resulting T will be in newton meters.

When I do the conversion of 280 lds per ft^2 to 8.75 slugs per ft^2 all of the numbers agree weather I use Imperial or Metric inputs in the motion physics formulas.

Kilograms per square meter of Inertia comes out as Newton Meters of Torque.

Slugs per square foot of Inertia comes out as Pound Feet of Torque.


We are re-conducting the drop-test using string wrapped around the flywheels axle shaft, with a pulley at the top of the garage for the longest fall distance we can make happen.

Thank you very much to everyone's assistance!

[Pursang]

There are really good reasons that Science and the rest of the world use the metric system (S.I. Système international d'unités.)

[F5 Dave]

Michelin tyres and the SI system. Best things to come out of France.

[diesel pig]

Michelin tyres and the SI system. Best things to come out of France.

You mean the only good things ever to come out of the land of terrible latin.

[husaberg]

Hi I was talking to a gentleman today at Ruapuna
He asked about what aluminium to use for sleeves to be plated.
Also about CF rotary valves and clearances.
He has posted on here.

I remember either Wob, Neil , Rob, or maybe Yow using specific a grade I think 2040? or similar that was fee matching an took the replating well?
I had a man look but TBH I am beat after only a few hours sleep and 600km travel today.

Good to see the Kr250 out looking all green and mean and a fair few TZ or close analogues.
My son is finally running comparable times on the Honda well......4t compared to the old Supermoto.
clean holeshot in all races and clean and tidy lines with the bike staying on the track.
I was hoping to catch up with DP. but missed him.

[husaberg]

Michelin tyres and the SI system. Best things to come out of France.

Didn't they invent the white flag or at least popularise its use? Pretty sure they also did a lot of developments work with scuba diving, limpet mines and zodiac dinghies...

[F5 Dave]

As I get older and more exposed to the Internet I realise that people are people and generally good sorts. It's the government's that tend to cause the trouble, and their's have been dreadfully damaging.

[Peter1962]

Didn't they invent the white flag or at least popularise its use? Pretty sure they also did a lot of developments work with scuba diving, limpet mines and zodiac dinghies...

They are great neighbours, but when it comes to inventing really important stuff they are no match.


https://www.compass-group.be/en/stor...gian-invention

[Storbeck]

Can't argue with the waffles. And FN Browning.

LeMans should count for something I suppose?

[F5 Dave]

And the croissant. . . Oh. That's from Austria.

[katinas]

Hi I was talking to a gentleman today at Ruapuna
He asked about what aluminium to use for sleeves to be plated.

Heat treated A6061 T6 containing magnesium and silicon as its major alloying elements and easy to find.

[wobbly]

Yes 6061 T6 in 8mm is what I will be using for the added plate on top of the KR180.
Is not available in 8mm plate so was sliced off a 127mm bar , CNC machined and bored /drilled to suit.
It has 0.2mm extra height to be take off after welding around the bore and the water jacket

[diesel pig]

So are two holes either side of the top stud hole for the coolant? are you happy that they are large a enough?