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Formula for a Motorbike Wheelie

INTRODUCTION
In the CB400 thread on Netrider, Positron007 speculated that the CB400 (which accelerates really quickly to 70kph) accelerates as fast as a 600cc sportsbike, at least up to the first gearchange.
He speculated that the limiting factor (up to 70km/h) was not the power of the bikes (which are vastly different) but the fact that you’re trying to prevent the bikes from doing a wheelie for this whole time.
So today, I thought I’d use my nerd powers for good instead of evil, and take a crack at explaining a wheelie formulaically. I couldn’t really find anything explaining the physics behind a wheelie on Google, so I thought I’d have a crack at it myself.
Disclaimer: May be wrong.
TL;DR: Positron is right, 600cc bikes don’t really accelerate faster (to 70kph) than the CB400.

 

ASSUMPTIONS
Assumption 1 – That both the CB400 and the 600cc sportsbike (which I’ll call the CBR600RR from now on) are both at their ‘liftoff point’ for the whole drag-race (which will be up to 70km/h, after which the CB400 is not capable of wheelie-ing).
Assumption 2 – The CB400 weighs 270kg fully laden with 76kg rider, and it’s COG (with rider) lies 600mm and 500mm from the rear axle.
Assumption 3 – The CBR600RR weighs 273kg fully laden with 76kg rider, and it’s COG (with rider) lies 650mm and 550mm from the rear axle.
Assumption 4 – Gravity is 9.81 m/s2

 

DISCUSSION
Why is the liftoff point important? A bike is accelerating at its fastest when the front wheel is at the point of becoming weightless. If the bike is accelerating any faster than this, then the front wheel will continue to lift off the ground, until the rider is on his back. (See endless YouTube videos to see this effect in action).
At liftoff point, both the liftoff and the gravitational turning moments are equal. What do I mean by this?

Moments

To describe this as a formula:

Moment (downwards) = Moment (upwards)

Aside:
I don’t think that this formula applies to drag-cars and other very-high performance vehicles. The principles do apply, but they also have some massive lifting forces created by the torquing action on their drivetrain. Bikes do not have torque-induced lift, especially at the low-power levels we’re looking at here.

The turning moment is the force multiplied by the perpendicular distance to the turning point, and can be described by the formula:

 Mt = F * D

To show the turning moments visually:

Horizontal Turning Moment

Horizontal Turning Moment

Vertical Turning Moment

Vertical Turning Moment

Force is described by the formula

 F = m * a

So, to combine all these equations

formula_1

Solving for acceleration provides:

formula_2

This is quite an interesting result, as the mass cancels out of both sides. Ergo, the mass of the bike has nothing to do with the bike’s ability to keep the front end off the ground. (Naturally, the bike’s mass will have a lot to do in limiting the amount of acceleration available to the bike.)

So it all comes down to the D(h) against D(v) ratio. In retrospect, this makes sense, as it is well-known that an adequately powerful cruiser can out-accelerate a sportsbike, due to its low COG and long wheelbase (more forward COG).

 

CONCLUSION

So comparing the CB400 against the CB600RR:

Result_CB400 Result_CBR

 

So the CB400 will actually out-accelerate the CBR, though there is not much in it. These accelerations will mean that the bikes will do 0-70km/h in 1.7 seconds. NOTE: The numbers for the vertical and horizontal distances are pure guesswork. Any assistance to provide real numbers would be greatly appreciated.

 

In Summary:

  • The maximum acceleration threshold for a bike is limited by its turning moment.
    • At any point below this threshold, acceleration will be limited by other factors, such as power, gearing, weight, etc.
    • The turning moment is a factor of the height and distance of the COG of the Bike (and rider) from the rear-axle.
    • Any two bikes which have sufficiently similar COG distances will have the same maximum acceleration threshold.

Review: Motolegion Jeans by RHOK – a disappointment

Introduction

Motolegion are a brand of jeans designed by Australian brand RHOK. I recently purchased a pair, and this is my review of them.

For the purposes of this review, I’ll be comparing the jeans against some work-issued jeans that I have – some King Gee jeans.

King Gee’s (left), RHOK (right)

Ordering and Delivery

Ordering was very simple from the RHOK website, though the website seemed confused as to how much the jeans were – the page said $145, but the Paypal checkout said $146.

Once I placed my order, I waited for 11 days, with no jeans in sight. I sent off an email, and was quickly replied to by Marinko. They were out of stock, but had forgotten to let me know. They said that they would ship the jeans in a couple of weeks. A couple of days later, however, I received another email, saying the jeans had been mailed, but they had probably sent the wrong size.

When the jeans arrived, they were indeed the wrong size. Marinko was very apologetic, and immediately sent up the correct size jeans, and a pre-paid express post satchel to send the wrong jeans back.

First Impressions

My first impression of the jeans was how thin the material was! I was expecting a very heavy, thick denim, but the denim felt a lot thinner and flexible to my fingers than the King Gee’s. A measurement with my micrometer confirmed by suspicions – the RHOK’s measured at 0.77mm vs the King Gee’s at 0.93mm. This obviously doesn’t matter from a protection standpoint, as the Kevlar does the protecting, not the denim, but the jeans may not last as long as I’d hoped.

What the jeans lack in thickness, they definitely make up for in weight. The King Gee’s weigh in at 804 grams on the scale, the RHOK’s are 1.10kg! I don’t know where the weight comes from – probably the kevlar panels, and the huge amount of thread which has gone into stitching these jeans together.

The stitching is very heavy duty. I’ll comment more on it later.

Stylin’

The jeans are not subtle at all. Red stitching all around, and a giant logo on your ass. If there was one aspect of the style of the jeans that I could live without, it’s the logo. Given that I usually wear work-issued jeans most of the time, and these come with the corporate logo on the back, I’m not totally adverse to this idea. However, the sheer size of the logo is off-putting.

Giant Ass Logo

Some of the panels, such as above the knee, and the seat also come pre-distressed. The ‘blue’ colour is also very dark. While not black it’s definitely on the ‘navy’ side of blue.

Distressed panels

Cut

The jeans are quite long, about 1cm longer than the 87R King Gee’s, which are a very traditional 501’s – style cut.

They’re also quite wide at the boot. You’ll have no trouble at all fitting these over your Sidi race boots. Each leg averages about 1cm wider when laid flat.

Width and colour difference between the two jeans.

The belt loops are a little bit narrow in length. My belt just squeezes through.

Stitching

The stitching is extremely heavy-duty. All of the important seams are triple-stitched. One area of concern is that all the stitching is external, and doesn’t have the ‘two under, one over’ style that is found on other jeans – like the King Gee’s. This raises a slight concern that in a bad slide the stitching may possibly wear through, though this seems highly unlikely, given the strength of the stitching.

Ultra-heavy-duty stitching

Internal Stitching, RHOK’s

Internal Stitching, King Gee’s

Each stitch has a massive amount of thread going through it. I’d like to know just what percentage of the weight of the jeans is made up of thread!

Comfort

On the bike – When on the bike, the jeans are perfectly comfortable, and don’t get in the way at all. However, I found that one of the seams appears to settle right on the inside of my knee, which is uncomfortable when hugging the tank. When I sit on the bike, I need to spend a second to make sure that the leg is rotated so that the seam is out of the way.

Off the bike, the jeans are surprising uncomfortable. The main culprit is the velcro panels inside the knee pockets. Because they face towards the outside of the jeans, the velcro strip  basically sits against your leg, tempered only by the thin mesh material. The sharp edges (especially the corners) of the strip poke through the mesh, and onto your leg.

This isn’t unbearably uncomfortable, but it’s pretty much continuously noticeable. I’m hoping that they soften up with wear and washing.

The Kevlar panels themselves are completely comfortable. You won’t even notice that they’re there.

Protection

The Kevlar protection is excellent, huge panels of kevlar weave covering all parts which are likely to slide along the ground in an accident. All the panels are the same size as the denim panels, and stitch into the same seams.

The hard protectors are highly weird, when compared to my other pair of riding pants (Motoline textiles). They are a standard ‘hard plastic over breathable foam’ style of protector. The knee protectors are a standard shape.

The shape of the hip protector, however, seems all wrong. They look like they have come out of a jacket, not a pair of pants. For comparison:

This is a side-by-side with the knee / elbow-forearm protectors from my Spidi jacket next to the shoulder / hip protectors from the jeans. The shoulder / hip protectors are nearly identical in shape.

Perfectly fitting ‘hip’ protector

When the hip protectors are in place, it makes you look like you’re wearing jodhpurs – it gives you fantastically wide hips. The protectors just stand out from your body, and don’t conform at all. There is a good centimetre of air from your body to the protector in the middle of the hump.

By comparison, here’s the hip protector from my Motoline textile pants.

One of these is designed for human hips.

The knee protectors can be inserted and removed through cleverly designed hidden zips below the knee.

The knee protectors go into mesh pockets that have ‘hook’ velcro on the bottom of the pocket. In addition to causing the comfort issues mentioned above, they also destroy the pocket itself. Every time you open the pocket, the hooks on the velcro tear at the mesh, which in my case is already starting to fuzz up from the abuse.

Knee pocket with Vecro ‘hook’ side up

The knee protector pockets are massive in the ‘up’ direction – they go halfway up my thigh. However, they’re not long enough in the ‘down’ direction. When I fit the pads so that they’re comfortable with a bent knee, the pads stick out the bottom of the pocket, so that the pocket can’t be done up! This is an epic flaw in the design.

They fit just fine if I rotate them 180 degrees, but I think they were meant to protect the shin, not the thigh. At this point in time, they’re just not usable. I’m going to either have to cut the knee protector with a Dremel tool (not a generally good idea, since it’ll leave some sharp edges), or buy a more standard foam protector and cut it to shape.

Summary

I bought these jeans hoping to ride them to work every day, to pop out the knee pads, and then work all day. As it stands, I can’t see myself doing that.

The knee pads are too difficult and time-consuming to put in. The hooks on the velcro also tear up the mesh extremely rapidly. Taking the protectors out once or twice a day is going to destroy the mesh in very short order.

I have two options – ride to work with the protectors in, then change to a different pair of pants. If that’s the case, I may as well wear a pair of waterproof textile pants. My second option is to ride without the protectors in place. That’s the option I’m taking at the moment, though riding without knee protectors is a concern.

The style and cut of the jeans seems aimed at a younger market segment. This is not a bad thing, but something to be aware of if you’re interested in purchasing these jeans.

Overall, I’m disappointed in the jeans. They’re not as good as I was hoping for, in comfort and practicability. I honestly can’t see myself buying another pair of these jeans, unless some of the recommended changes below are made.

Recommendations

Please note, that these recommendations are only based on my personal experience and tastes – YMMV. These are in order of my preference.

1. Fix the knee pad pockets or protectors, so that they actually match each other in size.

2. Remove the ‘hook’ velcro on the inside of the mesh pocket. Replace it with ‘loop’ velcro on the top side of the mesh pocket, then allow the owner to decide if they want to attach the ‘hook’ side to the protector.

3. Have a hip protector that is actually designed for human hips.

4. Have a second ‘subtle’ jeans style, for those who don’t want a giant logo on their ass.

5. Have a jeans style that has a more traditional tapered leg cut.

6. Make the belt loops about 3mm longer.

New Toy

I haven’t been posting much lately (I’ll go back in time and fill in some details retro-actively).

But here’s a photo of my new toy.

It’s a Honda CB400. Interestingly, it looks like the colour scheme is a homage to the old Honda CB1100R from 1983.

QRide

For Father’s day my ‘kids’ gave me the gift of some motorbike riding lessons. I did it with Toprider, at Rockhampton.

It was a really good course, done on a go-kart track. The track was great, as it allows you to practice all the elements of riding a low speeds.

I did the course over two days. On the first, I rode an Honda CB250. On the second, a Yamaha 400cc. The Yamaha was much heavier than the Honda, but I definitely enjoyed the extra power!