Another Human Powered Vehicle! Part 14 - New Rear Suspension

This article was first published in AutoSpeed.

Last week in Part 13 of this series I described how testing had shown a problem with the back wheel. When cornering on long, bumpy and fast (ie downhill!) sections of road, the rear wheel would patter sideways – something very disconcerting when you have only a very short wheelbase...

After considering tyre and spring natural frequencies, I’d decided that it wasn’t a damping issue but instead it must be the rear suspension arm torsionally winding-up and unwinding over cornering bumps. I’d tried hard to make the rear suspension arm stiff in torsion, but it looked as if I hadn’t succeeded. So how torsionally stiff was the design – and could it be made stiffer?

Testing

Assessment of the stiffness of the current rear suspension was required. But how to do this? I thought of mounting a video camera pointing downwards at the rear suspension arm, or mounting potentiometers or strain gauges. But by far the simplest approach was to use a pen and paper – almost literally!

I mounted a long vertical arm on the rear suspension. This arm projected upwards and through the rear carrier. On the end of the arm I mounted a whiteboard marker. The marker pressed against a piece of white laminated chipboard mounted on the carrier. The marker was held in contact with the board by means of an extension spring.

As the rear suspension arm moved up and down, the marker drew a vertical line on the board. Any torsional twist in the rear suspension caused the marker to move sideways. At 50cm in length, the arm was about twice the radius of the wheel, so the sideways movement of the marker was about twice the sideways movement of the tread on the road.

This close-up of the board shows the results of throwing the trike around (including two-wheeling). The width of the scatter of points (arrowed) is about 15mm, implying a lateral tread movement of about 7.5mm. Do the geometry calculation and that’s a total torsional twist of just 1.7 degrees! However, the testing wasn’t done travelling down the long bumpy hill at high speed. Also, if I physically held the trike and then grabbed the top of the wheel and pulled it sideways, a greater amount of torsional movement could be seen.

Stiffening

The first step was to try to stiffen the existing design.

I removed the rear suspension arm. The forward cross-piece (arrowed) was no longer required – it was initially installed to support a bump stop which testing had shown was (probably) not needed. However, the semi X-shape of the rear suspension arm gets a lot of its torsional stiffness from the way the two parts of the X are joined at their centre – and removing one of the cross-braces reduces the strength of this join.

To make a stronger join, in fact one stronger than the original, I inserted a 1.6mm chrome moly steel plate as shown here by the green highlight. Tested on the ground this clearly increased stiffness but when reinstalled on the trike, the old ‘yank the wheel’ test still showed plenty of movement in the rear suspension arm.

Identifying where this movement was happening was difficult, but some appeared to be occurring across the leading part of the arm. I then brazed-in a brace as shown here. But it made no difference to the on-trike stiffness.

Start Again

Reluctantly, I then decided the whole rear suspension arm needed to be redesigned and rebuilt from scratch. But hold on! What about the wonderful X-factor described so lovingly in Part 10 of this series? Was all that misinformed or misdirected? The answer to that is ‘yes’ and ‘no’.

Firstly, without any doubt the X-brace design gives improved torsional stiffness over a simple ladder frame. However (and as shown in that original article), if it is to be stiffened as much as possible, the arms of the X must extend right to the ends of the frame. In the case of my design, this did not (and cannot) occur. Secondly, the integrity of the central join is vital – my design was lacking in this area. And finally, and this is a big one, the tube I used was simply not stiff enough for the forces involved.

An indication of the latter can be gained from an experiment I did. I bolted the rear wheel in its drop-outs and then clamped the suspension assembly in a big vice, with the vice gripping the suspension arm at the spring location (ie as close to the wheel as possible). And even with the suspension arm reduced to just the rear ‘forks’, there was still some torsional twist visible. In other words, the tube simply needed to be stiffer.

Comparing Tube Stiffness

If all that you are doing is comparing torsional stiffness of different tubes, the maths is surprisingly easy. There are two factors to take into account – the wall thickness of the tube and its diameter. The tube that was used to construct the first rear suspension was 22.2mm in diameter with a 1.2mm wall thickness. Torsional stiffness is proportional to the wall thickness x diameter x diameter x diameter, that is, wall thickness multiplied by diameter cubed. Therefore, the stiffness is 13,129 (units don’t matter in a ratio comparison). So what if I went up in tube size to 35 x 1.2mm? The stiffness factor calculates to 51,450 – a stiffness that’s nearly four times as high!

Interestingly, the maths is also the same when comparing bending stiffness. Therefore, a good feel can be gained for the relative stiffness of different tube diameters and wall thicknesses by doing just a simple calculation.

And it gets even better. Working out the relative mass of the different tube sizes can be found simply by multiplying the diameter by the wall thickness.

(Note: all these calculations are approximations that apply to only thin walled tubes. RS Edgar provided the engineering expertise.)

So what do the figures look like when a number of different tube diameters and wall thicknesses are compared?

Tube Size (mm)	Stiffness	Stiffness Change over Original	Weight	Weight Change over Original	Stiffness/Weight Ratio
22.2 x 1.2	13129	-	26.6	-	494
32 x 0.9	29491	2.3x	28.8	1.1x	1024
35 x 1.2	51450	3.9x	42	1.6x	1225
44.5 x 0.9	79309	6.0x	40.1	1.5x	1978

This is a pretty stunning table. By upsizing to 44.5 x 0.9mm tube, the weight is half as great again – but the stiffness increases by an incredible six times! Or, looking at the 32 x 0.9mm tube, the stiffness increases by 2.3 times but the weight is only 10 per cent greater. And as can be seen from the Stiffness/Weight Ratio column, the bigger the tube, the greater the strength you can get for a given weight.

Clearly, it makes sense to use the smallest wall thickness / greatest diameter tube that is available and can be fitted into the space. The only caveat is that, to avoid wall buckling, the loads must be carefully fed into the whole tube, not just one part of the thin wall.

New Design

So, having absorbed all that – what next? The original rear suspension design was made in the largest diameter tube my small bench tool can bend. Anything bigger would either need to be commercially bent (and it’s very hard to find good benders that have the tooling for such small wall thicknesses) or use a different trailing arm design. Any new design would have to still match the existing position of the suspension pivots, wheel axle and spring location. In addition, clearance to the chain and frame would need to be maintained.

If the original design layout was followed (say with brazed joints where previously bends were used), any increase in tube weight would increase overall weight. Yes, stiffness would be up – but so would weight. On the other hand, if vastly stiffer tube was used, the design could be changed so that less tube was needed. On that basis, overall weight would not rise excessively.

In a move designed to radically boost rear suspension arm stiffness, I went for the largest tube available to me with a 0.9mm wall – 44.5mm. As shown in the table above, this has six times the stiffness of the original tube size but it weighs 50 per cent more. However, the rearmost section of the suspension arms (the rear “forks”) could not be made from this 44.5mm tube – there simply wasn’t the clearance. But I figured 32 x 0.9mm tube could be used, carefully flattened and shaped to appropriately join to the rear lugs (“dropouts”) and clear the chain. This tube has 2.3 times the original stiffness and weighs only 10 per cent more than original.

So with 44.5 and 32mm tubes, stiffness would be way up – but weight would also increase. So how to reduce the amount of tube required? After juggling various designs, I decided to go for a completely different approach to the previous trailing arm. In the new design a ‘Y’ section connects to the two forward mounted suspension pivot points. The upright of the ‘Y’ is extended rearwards to a crosspiece that mounts the rear ‘forks’. The Y and crosspiece calculated out as requiring 105cm of tube, which would all be in the large diameter 44.5mm. The rear forks needed about 60cm of 32mm tube. The total weight of the tube is 1050 + 400 = ~1450g. Add the two dropout lugs at ~200g and another ~150g for the bearings and bearing supports and you’re looking at around 1800g. The original rear suspension arm weighed 1.5kg, so at 1.8kg the proposed new design would be 17 per cent heavier.

Construction

Construction of the new arm was straightforward, except that the leading end of the ‘Y’, where the arm connects to the suspension pivots points, needed to use short lengths of 22.2 x 1.2mm tube to allow the arm to be positioned downwards for chain clearance. This looks a bit ugly but degrades stiffness very little (the tubes are only about 30mm long and are placed in compression/extension when the suspension is subjected to torsion). In fact, talking about aesthetics, the new rear suspension is clearly not as elegant as the previous design.

But has it solved the rear wheel patter problem? We’ll find out next week.

The Kamikaze Test Rider As a subscriber to a recumbent trikes mail list (ie a discussion group run by email), I occasionally get people wanting to ride my trikes. Someone from overseas or interstate might be in my area, and email me a request. Usually, such a request doesn’t gel with my plans or the stage of construction the trike is in. However, one day I got a ‘ride request’ and it seemed that it would work – the new rear suspension design had just been finished and the trike was ready to go. And I was very curious as to what another recumbent trike rider would think of my design – whether, for example, they’d immediately identify a shortcoming that I was so familiar with I could never see. The youngish bloke – I’ll call him ‘Ben’ – duly arrived. I described to him the front and rear suspension, and then demonstrated the trike by riding around the cul de sac on which I live. I went up on two wheels, cycling a big circle. Then, back on three wheels again, I rode over some bigger bumps formed where neighbours’ concrete driveways cross the grassy verge. I then offered Ben a ride. He donned my helmet and then immediately started pushing the machine fairly hard – within moments he was riding over the driveway bumps and drop-offs, picking a route that gave even bigger bumps than I’d traversed. It was interesting as a bystander seeing the behaviour of the trike: I had not seen it ridden in this way by someone of similar mass to me. “Throw it around a bit here,” I said – pointing to the flat and smooth bitumen of the cul de sac. Ben rode forward at a fair speed – say 15 km/h – and then banged on some steering lock. The trike immediately came up on two wheels. He then turned around, rode in the other direction, travelling even faster. This time he yanked on steering lock as hard as he could. The trike immediately rolled. Ben held out one hand to stop himself turning right over as the front right wheel hub gouged a 1.5 metre line in the bitumen. Besides his hand and the wheel retaining bolt, the other part sliding along the road was the rear derailleur. Apart from deep scratches, the trike was undamaged. After he picked gravel out of his hand, Ben also appeared undamaged. Now given that in skidpan testing – performed on just the same surface – I’ve exceeded the lateral acceleration of any other recumbent trike I have access to, the fact that my trike rolled is not indicative of a lack of cornering prowess. But what it does show – and especially since at the time Ben rode the trike, the road surface was damp – is that the front-end grip is very high indeed. Bang on lock and this trike doesn’t scrub straight on – instead the tyres grip and you start cornering! And, as with all recumbent trikes, if you corner hard enough, the trike will lift the inner wheel. Corner even harder and it will roll. And here I was thinking that, since I changed the steering to give toe-out in bump, turn-in performance had been reduced ...