Building Bicycle Wheels

Structure

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, ...

Three loads

• radial
• lateral
• torque — pedaling and hub brakes

Radial loads

• e.g., coasting in a straight line
• rim is flexible
• bends in slightly
  • temporary flat spot
  • temporary — "elastic"
• spokes near ground get
  • shorter
  • looser

Load support

• 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

Load distribution

• 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

Side loads

• Example

  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°
  • "potato chip"
  • "taco"
• 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

Spoke tension

• detensioning holds load
• so: "more is better"
• higher tension → higher load capacity
• except...
  • too much will buckle the wheel
  • or pull spokes out of hub or rim
  • or twist/damage skinny spokes when tensioning

How high?

• 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

Dishing

• 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

Less dish

• 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

• Example

  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 half up half down 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?

• yes
• spokes are strong enough to pull out
  • hub flange
  • spoke bed

• 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)

Fatigue

• 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

Stress relieving

• 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

Load-carrying summary

• 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

Requirements

What wheel to build?

• strength
• durability
• aerodynamics
• weight
• aesthetics
• purchase price
• operating cost

Your needs

• rider+bike+equipment weight
• kind of riding
• style of riding
• service life expectations
• risk tolerance
  • inconvenience/cost
  • 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
• iffy
• but lack of published data

Requirements and desirables

• requirement: "this is what the wheel must do"
• desirables: "goals that would be nice"
• quantify
  • "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
• vs.
  • under 1450g
  • aero-section rim
  • under 1400g
  • double-sealed bearings

Choose

• gather component info
• on paper, build hypothetical wheels
  • meet all requirements
  • some but not all desireables
• compare
• choose
• ... for lack of data, lots of "gut feel"
• process
  • 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

Lacing pattern

Lacing

• radial okay if no hub torque
• but need cross lacing if torque
  • rear wheel
  • disk brakes
• cross-lacing even if no torque load
  • one spoke length all places
  • (simplifies carrying spare spokes)
  • helps keep spokes from going slack
• interlaced
  • 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