The "A" Factor

TwoManyXS1Bs

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Just another cabin fever diversion.

The scenario is simple. You're emerging from a mild cruise toodle in a metro area, to the open highway. Or, you're wanting to pass around a slow truck. And, stay in 5th gear. What kind of acceleration can be expected when throttling up from about 45mph to 70-80mph, all while staying in top gear?

You and the bike present a total mass that has to be accelerated. The engine produces torque that's multiplied by the primary, trans, and final drive. An overall ratio that applies torque to the rear wheel, which produces a forward thrust to accelerate you and your bike.

The premise here is oversimplified, but somewhat reliable. Amazingly enough, a well designed 4-stroke motorcycle engine, in good condition and tune, will produce a torque value in ft-lbs that almost equals its displacement in cubic inches. Our 40 Cubic Inch XS650 engines should produce roughly 40 ft-lbs of torque, in the low to mid-range rpm zones, about 45-75mph in 5th gear. Outside that zone, the effects of restriction, reversion, and scavenge supercharging, provided by the cam and breathing systems, will affect the engine's volumetric efficiency (VE), and will nudge the torque value up/down a bit. Similar for other engines.

As an example, this early XS1 performance chart shows a torque curve that's somewhat depressed until it reaches higher rpms, attaining its 40 ft-lb torque, attributable to the more radical early 256 cam.
256-Performance01.jpg

This dyno chart, provided by member Crashcourse, shows the flatter torque curve (tan line) of the later 447 engines, just below 40 ft-lbs.
XS650SG-Dyno.jpg

Dyno charts of other bike engines also show a close relationship of displacement to torque. Some of the newer, hi-tech engines show nominal torque values a bit above their displacement size, attributable to the advancements in engine tech.

If you ever study a dyno chart, and see torque values that violate this general relationship, be suspect.

So, wanting to keep this thing simple, I chose to do comparisons based on engine displacements, expecting their torque values to comply with this general concept. The alternative would have been to acquire realistic torque charts, and convert them to a lookup table. The various, wild, and inconsistent published charts out there make that impossible, from my end anyway.

So, gyrating around with the physics and math, conversions, accommodations for rolling and wind resistances, wheel sizes, the whole complicated formula boiled down to a conveniently simpler version that closely predicts the expected acceleration within the typical tall-gear cruise region, of about 45-80 mph.

A = Acceleration in MPH per second
CC = Total engine displacement in Cubic Centimeters
TGR = Top Gear Ratio, the overall drive ratio from engine to rear wheel
BikeWt = The actual curb, or wet weight of the bike, in running order
RiderWt = Total weight of the rider, plus all the things worn and in pockets

BikeWt + RiderWt = The overall total weight of this thing that's rolling down the road

A = CC * TGR / (BikeWt + RiderWt)
 
So, I compiled a list of bikes I'm very familiar with, some vintage bikes, and some new bikes that have caught my attention. The idea here is to have another comparison tool, to see what's out there, what they have to offer.

This spreadsheet shows my bikes first, followed by some vintage models, then the new models. The 4th block of bikes are those that have 6 gears, and show what their "A" factor would be if remaining in 5th gear, with a rider philosophy of relegating the 6th gear to only high-speed constant cruise modes.

FactorA.jpg


The 2 cars at the bottom can be ignored, since I need to confirm their gearing.

If the "A" factor is 5 or greater, it's shaded in yellow.
If the "A" factor is 6 or greater, it's shaded in red.

My 'ol XS1B chopper was quite a pleasure to ride, achieving a factor of 6, and would be my personal target minimum. A factor of 6 means that you could go from 45mph to 70mph in 4 seconds. Quite pleasurable, no need to downshift...
 
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Love your math "doodling" 2M.
I have a definite fondness for "tractor like" torque at low RPM. However....
I have owned a couple Prius, they make large torque from a standstill with the electric motors developing full torque at 0 RPM. Oddly they offer none of the satisfaction of a large displacement gasoline motor chugging away where you can feel and hear individual power pulses. The 1100 Shadow Aero was my favorite for this even though it was distinctly lacking in horsepower even by lax v-twin standards. A ramp cam in the drivetrain reduced the abuse factor and the large volume muffler produced a lovely chuff chuff chuff as it motored off. This predilection might be inherited. My dad was famous for feeding out pickup truck clutch at very low RPM, low enough that rod rattle was prominent. I would cringe on hearing that, but will push madness to torque off from a stop just above that rattle zone. :rolleyes: :cool:
I also worked to change the engine torque / horsepower curve on madness to favor better low RPM numbers rather than "wound out" HP.
amazing how much different your Dragon is from a stock XS60D.
Doodle on 2M:D
 
It seems like most racing with other bikes on the highway happens between 45-70 mph...
Knowing that it's not especially easy to pass something already going 45 probably makes it a safer bike... Makes your behavior safer I mean.
 
Just another cabin fever diversion.

The scenario is simple. You're emerging from a mild cruise toodle in a metro area, to the open highway. Or, you're wanting to pass around a slow truck. And, stay in 5th gear. What kind of acceleration can be expected when throttling up from about 45mph to 70-80mph, all while staying in top gear?

You and the bike present a total mass that has to be accelerated. The engine produces torque that's multiplied by the primary, trans, and final drive. An overall ratio that applies torque to the rear wheel, which produces a forward thrust to accelerate you and your bike.

The premise here is oversimplified, but somewhat reliable. Amazingly enough, a well designed 4-stroke motorcycle engine, in good condition and tune, will produce a torque value in ft-lbs that almost equals its displacement in cubic inches. Our 40 Cubic Inch XS650 engines should produce roughly 40 ft-lbs of torque, in the low to mid-range rpm zones, about 45-75mph in 5th gear. Outside that zone, the effects of restriction, reversion, and scavenge supercharging, provided by the cam and breathing systems, will affect the engine's volumetric efficiency (VE), and will nudge the torque value up/down a bit. Similar for other engines.

As an example, this early XS1 performance chart shows a torque curve that's somewhat depressed until it reaches higher rpms, attaining its 40 ft-lb torque, attributable to the more radical early 256 cam.
View attachment 131447

This dyno chart, provided by member Crashcourse, shows the flatter torque curve (tan line) of the later 447 engines, just below 40 ft-lbs.
View attachment 131448

Dyno charts of other bike engines also show a close relationship of displacement to torque. Some of the newer, hi-tech engines show nominal torque values a bit above their displacement size, attributable to the advancements in engine tech.

If you ever study a dyno chart, and see torque values that violate this general relationship, be suspect.

So, wanting to keep this thing simple, I chose to do comparisons based on engine displacements, expecting their torque values to comply with this general concept. The alternative would have been to acquire realistic torque charts, and convert them to a lookup table. The various, wild, and inconsistent published charts out there make that impossible, from my end anyway.

So, gyrating around with the physics and math, conversions, accommodations for rolling and wind resistances, wheel sizes, the whole complicated formula boiled down to a conveniently simpler version that closely predicts the expected acceleration within the typical tall-gear cruise region, of about 45-80 mph.

A = Acceleration in MPH per second
CC = Total engine displacement in Cubic Centimeters
TGR = Top Gear Ratio, the overall drive ratio from engine to rear wheel
BikeWt = The actual curb, or wet weight of the bike, in running order
RiderWt = Total weight of the rider, plus all the things worn and in pockets

BikeWt + RiderWt = The overall total weight of this thing that's rolling down the road

A = CC * TGR / (BikeWt + RiderWt)


Haha, wow 2M, bored much..??? lol
 
... my FJ09 has the same incredible engine as the XSR900. No wonder I love that bike!

Oh, yeah, that cross plane 850 is the epitome of the ideal engine. Very flat torque curve, with a +15% nudge at the higher rpms.
XSR900-Dyno-04.jpg


With a torque value just above its 52 CuIn displacement, geared almost identical to the XS650, and light weight, it'll get the high "A" factor...

FonzieA.gif
 
...I have a definite fondness for "tractor like" torque at low RPM...

Haha, me too. I wuz hopin' to tickle an interest in this.

... The 1100 Shadow Aero was my favorite for this ...

Did a little research on the VT-1100 Shadow Aero, but can't determine its wet weight. Too many versions, showing 666lbs down to 566 lbs.

With a 220 lb rider, I get:
VT-1100 - 1099cc, TopGear=4.0, 666lbs ==> A = 5.0

About the same as the Star Bolt.

Using the lighter weight,
VT-1100 - 1099cc, TopGear=4.0, 566lbs ==> A = 5.6

About the same as the new Harley Low Rider, in 6th.

Then, I bumped into the Virago 1100 specs.

Virago 1100 - 1063cc, TopGear=4.8, 531lbs ==> A = 6.8 (!!!)

A real stump puller, although a high revver.
Even higher with a lightweight rider.

...I also worked to change the engine torque / horsepower curve on madness to favor better low RPM numbers rather than "wound out" HP.

Our XS engines are quite responsive to cam timings. Opening up the valve lash (errp) may boost the low end some more.

...amazing how much different your Dragon is from a stock XS60D.

According to this "A" factor formula, simply going to 750cc, plus a drop in weight, can get those high numbers. I'm sure there's some bobbers in here, with lightweight riders,that would show even better numbers...
 
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Just to put another perspective on this, the "A" factors don't seem to show much difference, until they're applied. For example, take 2 bikes, one a "5", the other a "6".

Both bikes in high gear, rolling abreast at 45mph.
Simultaneously go to WOT.

After 5 seconds, the "5" bike is doing 70mph.
The "6" bike has pulled ahead almost 20 feet, doing 75mph.

Both riders should be grinning...
 
The Aero is a special case of Shadow, 98 to 2000 Aero only has the offset pin crank for "genuine Harley" sound, but they detrated the HP from the other Shadows, losing 10HP was painful, then for 2001 they bumped it back up 10HP that was the last 1100 Aero.
In 97 Shadow 1100s went from a 4 speed to an overdrive 5th that is for 65MPH plus cruising at chuffa chuffa RPM only.
Had 4 different 1100s but never found an 01 Aero. A Shadow fan really has to dig into the specs to find the exact setup they want. Shaft drive so gearing changes aren't simple.
Talked to a guy bought a Honda CTX700 DCT (670cc 4 valve 270 crank parallel twin, dual clutch, shift button automatic) was really pleased with it. That's on my short list of want to try bikes.
 
I cooked up this thing to help evaluate and compare the current/modern offerings against my recollections of years ago, then it dawned on me. I didn't weigh that much back then.

This is what I like about spreadsheets. A couple little changes, and you get a whole new "whatif" list. The first 2 groups are bikes from the '70s, back when I weighed about 150 lbs. The 3rd group is new bikes that would have to carry my modern carcass. Took me a long time to gain that much weight, and that's the way it is. The 4th group is the 6-speed models in 5th gear. All groups are sorted in increasing "A" factor.

So, can anything in the new crop of bikes allow me to re-experience my youth?

FactorA5.jpg
 
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Justa little update.

I've been losing weight, and wanted to revisit this thing.

A comparison of just 4-stroke naked twins, air or air/oil cooled, street and cruiser.
Removed a couple of entries.
Added a couple of new bikes, Royal Enfield Interceptor 650, Kawasaki W800.
Added an XS1B and XS650D with 750 kits.

FactorA9.jpg


Notice how simply adding a 750 kit to an XS650 moves it up in the list...

Edit: Replaced the chart, sorted hi to low, rounded off the rpms...
 
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2M, you have proved the age-old assertion that the cheapest performance mod is for the rider to lose some weight.

My uni buddy Dungbeetle used to look at modified bikes where everything was drilled, or even replaced with expensive titanium parts, and suggest that you would save more weight by going for a waz before heading out.

Low-down torque is nice to have. Used to have a Victory Hammer. It was a long and heavy bike. But with 1736 cc of Murrican grunt. Felt good to just roll the throttle open on a long straight - gave the illusion that fat back tyre was turning the planet backwards under yer backside.
 
Very interesting charts Steve! Back in 2007 I purchased a Triumph Bonneville America, it weighed about 550lbs and had a displacement of 865cc, and I had done some performance mods to it.
All of my Harley riding friends, the first thing they asked was how big is the motor? When I would tell them, they would laugh like it was a beginner bike. I would always tell them, you gotta think about more than just displacement ! The power to weight ratio is what matters. It’s funny, I did a whole bunch of spreadsheets , sorta like yours but just doodled on a pad. :D What I soon realized is that my little cruiser was punching way above its weight class. It had a power to weight ratio closer to most 1200cc to 1300cc V-Twin cruisers. Add to that , my body weight was about 50 - 75 pounds less than most of my Harley riding brethren and the performance gap closed up even more.
I have been to very many factory demo ride events and I have ridden Everybody’s big V Twin cruisers. And it has helped me realize how much more fun ( for me anyways ) it is to ride a light weight good performing mid sized bike.

( If you want to see a power to weight ratio that is off the charts, you need look no further than a Hyabusa! )

Side note: I read an article a while back, an interview with one of the head design engineers at Ducati. He designed some of their best selling big performance bikes. What did he choose for his personal bike? The 696cc monster. ;)
 
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