Building Bicycle Wheels
Structure — how a wheel supports a load
- mental model: flat rim, radially spoked, tensioned
- a small lie: model doesn't always work
- good enough for now
Flex under load
- both rim and spokes flexible
- flex is small to the eye/hand
- big tension changes
- "In the real world, everything is made of rubber" — Jobst Brandt
- supports loads by bending the rim (temporarily)
- and loosening spokes (temporarily)
- constant motion — demonstration
- rusty eyelets
- click, click, ...
- torque — pedaling and hub brakes
- e.g., coasting in a straight line
- rim is flexible
- bends in slightly
- temporary flat spot
- temporary — "elastic"
- spokes near ground get
- load supported by difference in tension
- tension pulling up
- tension pulling down
- you can demonstrate this
- pluck a spoke near the ground
- have somebody sit on the bike
- pluck again — lower tone
- add up the forces
- 100 kgf load at hub
- 100 kgf load at ground
- 100 kgf reduction in vertical spoke tension
- across all spokes supporting the load
- spokes pointing at ground lose the most tension
- spokes near to ground lose some tension
- rim is flexible
- imagine extreme cases of very stiff and very floppy
- very stiff => tension changes at top
- very floppy => only one spoke changes tension
- in practice rim stiffness is "medium"
- spread over approx. 1/8 of rim (MA-2)
Side (lateral) load
- push sideways at ground
- bends rim slightly
- lateral "blip" — no longer flat (temporary)
- some spokes get looser
- some spokes get tighter — but not much
- load-carrying spokes already detensioned
- more tension → rim bends inward
- loosens other spokes
- load is supported by difference in tension
- sum across all spokes
- including lateral increase → radial decrease
Side loads more complex
- 10kgf side load → 10kgf change in "lateral tension"
- but spokes are nearly radial
- spoke tension is "leveraged"
- the "wrong" way
- small lateral force → big change in spoke tension
- 300 mm spoke, 30 mm flange offset (60mm separation)
- arctan(30/300) → 5.7 degrees
- 10 kgf lateral force
- 10 kgf / sin(5.7) = 100 kgf change in spoke tension
- spread over approx. 1/8 spokes
- bicycle wheels are laterally weak!
- usually not a big deal
- ... turn by balancing not by big lateral forces
- but not a lot of margin
Radial strength limit
- maximum strength: when spokes go slack
- push harder
- spoke nearest load: already slack
- no change in tension to resist more load
- load shifted to farther spokes
- (load has to go somewhere)
- large rim deflection
- with enough radial displacement → rim bends
- more likely: large radial load + small lateral load
- no lateral support (spoke already slack)
- rim moves laterally at ground
- leverage: rim moves opposite direction at 90°/270°
- often no permanent damage
- but wheel is a mess
- too wide to turn in the fork/frame
Strength is affected by stiffness!
- stiffer rim spreads the load across more spokes
- more flexible spokes don't go as slack for a given load
- spread load across more spokes
- some residual tension against lateral loads
- but no free lunch
- weight of stiffer rim
- spokes can be too flexible (more in a moment)
Summary — strength
- stiffer rim or more flexible spokes → radially stronger
- more spokes holding the load → stronger lateral and radial
- thinner (flexible) spokes
- often stronger for mostly-radial loads
- often weaker for mostly-lateral loads
- detensioning holds load
- so: "more is better"
- higher tension → higher load capacity
- too much will buckle the wheel
- or pull spokes out of hub or rim
- or twist/damage skinny spokes when tensioning
- usual limit: total rim compression
- pairs of opposing spokes...
- ... a ton of rim compression!
- some rims have rated max spoke tension
- e.g., Velocity will tell you if you ask(!)
- use tensiometer when building
- or discover it during wheel building
- many but not all rims
- don't need tensiometer
- more below
- rim not centered between hub flanges
- rear derailleur gears, front disk brakes
- spokes are at different angles → uneven tension
- slack spokes go slack sooner → weaker wheel
- compensate by overtensioning the tight spokes?
- pull spokes out of hub or rim
- or twist spokes
- round off nipples
- even if higher tension...
- ... poor bracing angles
- fewer sprockets on the right
- hard to just go out and buy
- asymmetrical rim
- "offset spoke bed"
Summary — tension and dish
- more tension → stronger wheel
- but too high leads to wheel failure
- use asymmetrical/offset spoke bed for dished wheels
- disk-specific rims rarely have an offset spoke bed!
Torsion loads — pedaling, hub brakes
- tangent spoking
- on torsion load
- half the spokes get tighter, half looser
- center spool is flexible
- 1/4 up, 1/4 down, 1/2 unchanged
- pedaling: change in tension usually small
- ... compared to tension changes from weight
- hub brakes: significant under hard braking
Torsion load from pedaling
- climb 5.7 degree (10%) grade at constant speed
- 100 kg bike+rider × sin(5.7) =10 kgf tangent at tire
- 333mm radius wheel, 33.3mm radius flange, tangent
- 10 kgf × (333/33.3) = 100 kgf spoke tension change
- spread over half the spokes (18)
- 100 kgf/18 → 5.5 kgf per spoke
- vs. many tens of kgf under rider's weight
- 100kgf typical spoke tension
- steeper grade? hard sprint?
- similar anlaysis
- similar result: relatively small change
Torsion load from hub brakes
- 0.1g acceleration 100 kg bike+rider = 10 kgf at tire
- same analysis: 5.5kgf spoke tension change
Maximum torsion load from braking?
- max deceleration: rear wheel just off the ground
- rider's center of gravity about as far above tire contact as behind
- so max deceleration approaches 1g
- 10& times; 5.5kgf → 55 kgf tension change in 1/2 spokes
- a lot!
- no weight on back wheel
- all on front wheel
- front disk brake wheels usually dished (weaker to start)
- weight "uses up" tension near ground contact
- spokes may go slack
- wheel near collapse
Hub brake recommendations
- very stiff center spool
- spread load across all spokes
- 26kgf tension change in all the spokes
- hub brakes need stronger wheels
- stiff rim
- plenty of spokes
- thin for load sharing vs. thick for lateral strength
- plenty of good solutions
- just not as light as rim brake wheels
Summary — hub brake loads
- "overbuild" front hub brake wheels
- rear not a problem — rear wheel skids at <0.5g
Are skinny spokes strong enough?
- spokes are strong enough to pull out
- Q: then why do spokes break?
- A: residual stress from manufacture
- when load is carried unevenly across spoke section
- (or if badly twisted during wheel building)
- technical term (not intuitive meaning)
- many unload/load cycles → fail
- strength vs. durability
- spoke is strong enough
- is not durable enough
- fails at load less than the strength(!)
- as little as a few months of riding
- "stress relieve" to even out load within spokes
- same parts → no broken spokes
- spoke manufacture: bend elbow
- imaginary "fibers"
- some parts yield — stretch permanently
- other parts stretch then relax
- an unlaced spoke has internal stresses
- tensioning changes the size of stresses
- but still uneven
- tension spoke
- overtension by squeezing pairs "vigorously"
- highest-tension "fibers" yield
- shares load better with looser "fibers"
- more about this soon
- wheel loads carried by reduced spoke tension
- load (strength) limit when spokes go slack
- more strength:
- stiffer rim
- more spokes
- radial: thinner spokes
- lateral: thicker spokes
- fatigue (durability) limit if spokes not stress-relieved
What wheel to build?
- purchase price
- operating cost
- rider+bike+equipment weight
- kind of riding
- style of riding
- service life expectations
- risk tolerance
- personal injury
- tires you use (rim width)
- how much wet riding (brake wear)
Let your experiences be a guide
- "my wheels go out of true all the time"
- "the wheel collapsed when I landed"
- "I keep breaking spokes"
- "the hub flange failed"
- "I wore out the rim sidewall"
- "tires are hard to install and remove"
- "tires blow off the rim"
- "my wheels are durable, I want to climb faster"
- "my wheels work fine, I want better aerodynamics"
- "my wheels look plain, I would enjoy bright colored rims"
- "somebody stole my wheels with shiny hubs"
Lack of published data
- rim makers do not report beam section info
- nor aerodynamic information
- rarely even maximum spoke tension for rim spoke bed
- you can measure brake track thickness
- maybe: thickness in box section?
- varying durability of different aluminums?
- hard to quantify
- can make some educated guesses
Let experiences of others be a guide
- mixed source of information
- if lots of failures → beware
- if not many failures ... why?
- could be: really good
- maybe: nobody really uses it that much
- observation error
- "bombproof!" — is rider 50kg or 100kg?
- ... do they carry groceries on the rack?
- ... do you?
- "never needs truing!" — compared to old wheels
- "I ride them hard!" — compared to potatoes
- but lack of published data
Requirements and desirables
- requirement: "this is what the wheel must do"
- desirables: "goals that would be nice"
- "strong" vs. "supports 150kgf bike + rider on 1-metre flat drop-offs"
- "durable" vs. "10 years service with only rim changes"
- "light" vs. "1500g for both wheels"
- "cheap" vs. "$100 maximum price"
- both requirements and desirables
- requirements are deal-breakers: meet them or don't build"
- rank desirables
- may overlap, may want to split
- double-sealed bearings
- under 1450g
- aero-section rim
- under 1400g
- under 1450g
- aero-section rim
- under 1400g
- double-sealed bearings
- gather component info
- on paper, build hypothetical wheels
- meet all requirements
- some but not all desireables
- ... for lack of data, lots of "gut feel"
- going through steps helps you refine your goals
- choices will be between several wheels that all meet goals
- so don't sweat it too much
- radial okay if no hub torque
- but need cross lacing if torque
- cross-lacing even if no torque load
- one spoke length all places
- (simplifies carrying spare spokes)
- helps keep spokes from going slack
- weaved in and out
- more complicated to build
- better support
- holds spoke if it breaks
Head-in or head-out
- head-in vs. head-out
- radial wheel
- head-in 2mm wider than head-out
- rears often head-out for more symmetry
- tangent spoke: mirrored vs. symmetrical
- torque loads
- tension change vs. rim lateral motion
- but small especially if flexible hub spool
- right rear: leading head-in or leading head-out?
- chain drop between sprockets and spokes
- leading head-in self-eject if pedaling, self-tangle if coast
- leading head-out self-eject if coasting, self-tangle if pedaling
- in my experience natural reaction is coasting → leading head-out
- or use a spoke protector