What limits us here is not really the weight, but being able to transport the load and remain upright. Ideally the load would be securely fixed somewhere just above the crank and directly below the saddle, indeed it could be very heavy but there is simply not enough space for anything more than a tin of beans. So to carry a worthwhile volume we need to compromise on weight and position whilst remaining within budget.
For light and bulky objects a rucksack is fine provided that the straps are tight and the load will not shift but for anything more than a few tins of ordinary beans is potentially dangerous.
A bum-bag will hold less but will be more comfortable to wear, and because the load is closer to the ideal centre, cornering will be safer.
Panniers are best as the bike carries the load not you, fitted appropriately and the load distributed evenly, 30kg or more can be transported with relative ease and if the rider is competent, safely. A set with bags is expensive and our aim is to travel short distances carrying maybe 16 tins of beans on meagre means, luckily there are alternatives to completely shop bought panniers.
Only a rear frame is needed, it must be robust and securely attached to the bike but doesn't need to be of the highest spec or new, and remember those that are rated as capable of carrying the lightest load will be light themselves.
The bag can be improvised from an old rucksack: the area around where the straps are attached to the rest of the rucksack must be in good condition, and when full or empty no part hang significantly below the rear axle, nor be so wide as to come into contact with rest of bike/rider.
Lay the opened rucksack facedown, loosen shoulder-straps and waist-strap. Position frame on top, pass end of strap under top rail of frame, looping over, pull tight, using small nail, make a temporary fixing through strap and back of rucksack, repeat with other strap, be sure that rucksack will not slide back and forth nor up and down. If so re-position.
Completing one side at a time: using large nail enlarge hole, ensure washer is fitted, from the inside of rucksack push bolt through hole, fit other washer then nut, tighten. Sever straps leaving enough canvas so they can be tucked under and glued.
The next stage may require a little trial and error. The objective is to tie the two ends of the waist-strap to the frame securely, thus final positioning of the panniers is achieved, only then is the frame attached to bike.
One side can be shorter and tighter, the other longer and slack. This draws pannier away from the riders' leg whilst allowing the pannier to be filled to capacity. However too much slack allows the pannier to flop about when empty. Fill the pannier with crumpled newspaper instead of tins of beans, tie the knot another way if not happy. Two clove hitches work fine, but remember to tuck in free ends of straps otherwise the knot will work loose, glue and trim ends when satisfied. Remember the legal requirements regarding reflectors, rear red, front white.
VERY IMPORTANT: a shifting load is a live load and will move with a mind of its own, fastening the load securely and packing of any bags in a thoughtful way is essential. Liquids will always be a live load if the container is not full to the brim and sealed.
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