Bijective proof: Difference between revisions

Latest revision as of 23:15, 19 March 2013

The wheel size for a motor vehicle or similar wheel has a number of parameters.

Bolt pattern

The bolt pattern determines the number and position of the mounting holes to allow the wheel to be bolted to the hub. As the bolts are evenly spaced, the number of bolts determines the pattern. For example: smaller cars have three (Citroën 2CV, Renault 4, some Peugeot 106s and Citroën Saxos, and the Tata Nano). Compact cars may have four bolts. Most United States passenger cars have five bolts. Pickup trucks and large SUVs can have as many as six, eight or ten.

Bolt circle

The bolt circle is the notional circle determined by the positions of the bolts. The center of every bolt lies on the circumference of the bolt circle. The important measurement is the bolt circle diameter (BCD),^[1] also called the pitch circle diameter (PCD).^[2]

Bolt pattern guide by manufacturer

A general guide to common bolt patterns by manufacturer:

BMW: 5x120 mm

Dodge: 5x100 mm, 5x114.3 mm

Ford: 4x108 mm, 5x108, 5x114.3 mm, 5X135 mm, 5X139.7 mm

GM (Chevy, Pontiac, etc.):5x100mm, 5x115 mm, 5x120.7 mm, 6X139.7 mm

Honda/Acura: 5x114.3 mm, 4x100 mm, 4x114.3 mm

Jeep Wrangler JK 07-UP 17"&18" 5x127mm 5x5in

Mazda: 5x114.3 mm, 4x110 mm, 4x114.3 mm

Nissan/Infiniti: 5x114.3 mm, 4x114.3 mm

Peugeot/Citroen: 4x108mm

Porsche: 5x130mm

Renault: 5x108 mm, 4x100 mm

Volvo/Jaguar: 5x108mm

Subaru: 5x100mm, 5x114.3mm

Toyota/Lexus/Scion: 5x114.3 mm, 5x100 mm, 4x114.3 mm

VW/Seat/Audi:5x100mm, 5x112 mm

This guide is accurate for most of the cars made by the listed manufacturers, but it is important to check and make sure before purchasing new aftermarket wheels.

The BCD may be expressed in millimeters or inches, and is usually given with the number of bolts. For example, a 1974 MG B has a 4/4.5 inch (4/114.3 mm) wheel hub, meaning it has a 4-bolt pattern with a 4.5 inch (114.3 mm) bolt circle diameter.

The most common BCD values are 100 mm (≈3.94 inches) and 4.5 inches (114.3 mm). Many old British cars use 4 x 4"

Special BCD values are: 95.25 mm (for MG F and Rover Metro), 98 mm (for Fiat group automobiles), 101.6 mm (for Mini, MG, Austin Metro), 100 or 105 mm (for some GM vehicles), 108 mm (mostly for PSA, Ford and Lincoln), 110 mm (for some GM vehicles), 112 mm (for Mercedes-Benz and some VW group vehicles), 115 mm (for some GM vehicles), 120 mm (mostly for BMW), 130 mm (for Porsche), 170 mm (for Saab 96). Old British Triumph cars used 4 x 3.75" using 3/8" studs. (7/16" or M12 studs are advisable for track use)

Determining the bolt circle

For a 4- or 6-bolt wheel, this measurement is merely the distance between the center of two diametrically opposite bolts. In the 4-bolt picture above, this would be the distance between holes #1 and #4, for example.

Some basic geometry is needed to find the center of a 5-bolt pattern. In practice, the BCD can be found by multiplying the center distance between any two adjacent holes by 1.701.

BCD geometry of 5-bolt pattern

\sin \left({\text{half top angle}}\right)={\frac {\text{center distance}}{2\times {\text{radius}}}}

or

{\text{radius}}={\frac {\text{center distance}}{2\times \sin \left({\text{half top angle}}\right)}}

half the top angle of a 5-bolt wheel is:

{\frac {360^{\circ }}{5}}\times {\frac {1}{2}}=36^{\circ }

using a unity center distance of 1, a bolt circle diameter = 2 × radius, and sin(36) = 0.58778:

{BCD}=2\times {\frac {1}{2\times 0.58778}}=1.701

Generally, the BCD b can be calculated for any wheel from the number of bolts n and the center distance d between two adjacent bolts as: $b={\frac {d}{\sin \left({\frac {1}{n}}180^{\circ }\right)}}$ .

A far easier way, using less math, is to take calipers and measure the hole size in the center of the wheel (note half of this dimension). Next measure the distance between the edge of the center hole and the center of one stud. Double this measurement and add it to the Noted sum. Job done! (That is determine the radius of the hole size, not the diameter) This method works with any number of studs.

Lug nuts or bolts

Wheels must be fitted with the correct type of lug nuts on wheel studs, or bolts. Lug nuts (aka wheel nuts in British English) are usually either flat, tapered (generally at 60 degrees and referred to as conical seat), or ball seats, meaning the mounting surfaces are flat, tapered, or spherical respectively.

Most Mercedes have ball lug seats from the factory while most aftermarket wheels have a tapered lug design. Wrong lug nuts for the wheel will not properly center it and cause wobble. Some manufacturers (e.g. Toyota and Lexus) have used taper lug nuts for steel wheels and flat seated lug nuts for alloy wheels.

Some aftermarket wheels will only fit smaller lug nuts, or not allow an ordinary lug nut to be properly torqued down because a socket will not fit into the lug hole. Tuner lug nuts were created to solve this problem by utilizing a special key to allow removal and installation with standard lug wrench or socket. The design of tuner lug nuts can range from bit style to multisided or spline drive, and are sometimes lightweight for performance purposes.

A variation is the "locking wheel nut", which is almost universally used for alloy wheels in the United Kingdom. One standard lug nut on each wheel is replaced with a nut which requires a special and unique key (typically a computer-designed, rounded star shape) to fit and remove the nut. This helps to discourage theft of wheels. However, universal removal tools are available which grip the head of the locking nut using a hardened left-hand thread. The success of these depends on whether there is room to use it in the lug hole, and whether the manufacturer has incorporated a free-spinning outer casing to the lock. Keeping an appropriate tool to lock and unlock aftermarket nuts, and a spare set of nuts, with the spare tire in the boot of the car is recommended by manufacturers.

Centerbore

The centerbore of a wheel is the size of the hole in the back of the wheel that centers it over the mounting hub of the car. Some factory wheels have a centerbore that matches exactly with the hub to reduce vibration by keeping the wheel centered. Wheels with the correct centerbore to the car they will be mounted on are known as hubcentric. Hubcentric wheels take the stress off the lug nuts, reducing the job of the lug nuts to center the wheel to the car. Wheels that are not hubcentric are known as lugcentric, as the job of centering is done by the lug nuts assuming they are properly torqued down.

Centerbore on aftermarket wheels must be equal to or greater than that of the hub, otherwise the wheel cannot be mounted on the car. Many aftermarket wheels come with "hubcentric rings" that lock or slide into the back of the wheel to adapt a wheel with a larger centerbore to a smaller hub.^[3] These adapters are usually made of plastic but also in aluminum.

X-factor

Caliper Clearance (X-factor): The amount of clearance built into the wheel to allow for the vehicle's disc brake and caliper assembly.

Load capacity

Load capacity is the amount of weight a wheel will carry. This number will vary depending on the number of lugs, the PCD, the material used and the type of axle the wheel is used on. A wheel used on a free rolling trailer axle will carry more weight than that same wheel used on the drive or steering axle of a vehicle. All wheels will have the load capacity stamped on the back of the wheel.

GVWR

This is the Gross Vehicle Weight Rating. In the United States this information is required to be on the vehicle's door placard. The load capacity of the total number of wheels on the vehicle combined must meet or exceed the vehicle's GVWR.

References

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@@ Line 1: / Line 1: @@
+{{multiple issues|
+{{Refimprove|date=December 2010}}
+{{Howto|date=September 2009}}
+}}
+The '''wheel size''' for a [[motor vehicle]] or similar [[wheel]] has a number of parameters.
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+==Bolt pattern==
+The ''bolt pattern'' determines the number and position of the mounting holes to allow the wheel to be bolted to the hub. As the bolts are evenly spaced, the number of bolts determines the pattern. For example: smaller cars have three ([[Citroën 2CV]], [[Renault 4]], some [[Peugeot 106]]s and [[Citroën Saxo]]s, and the [[Tata Nano]]). [[Compact car]]s may have four bolts. Most United States passenger cars have five bolts. Pickup trucks and large [[sport utility vehicle|SUV]]s can have as many as six, eight or ten.
+==Bolt circle==<!-- This section is linked from [[BCD]] -->
+[[Image:4hole wheel.png|right|thumb|4 Hole Pattern]]
+[[Image:5hole wheel.png|right|thumb|5 Hole Pattern]]
+The [[wikt:bolt circle|bolt circle]] is the notional [[circle]] determined by the positions of the bolts. The center of every bolt lies on the [[circumference]] of the bolt circle. The important measurement is the bolt circle [[diameter]] (BCD),<ref>{{cite web|title=Bolt Circle Diameter (B.C.D.)|work=Sheldon Brown's Bicycle Glossary|url=http://www.sheldonbrown.com/gloss_bo-z.html#bcd|accessdate=3 Dec 2010}}</ref> also called the ''pitch circle diameter'' (PCD).<ref>{{cite web|title=P.C.D.|work=Sheldon Brown's Bicycle Glossary|url=http://www.sheldonbrown.com/gloss_p.html#pcd|accessdate=3 Dec 2010}}</ref>
+Bolt pattern guide by manufacturer
+A general guide to common bolt patterns by manufacturer:
+BMW: 5x120 mm
+Dodge: 5x100 mm, 5x114.3&nbsp;mm
+Ford: 4x108 mm, 5x108, 5x114.3&nbsp;mm, 5X135 mm, 5X139.7&nbsp;mm
+GM (Chevy, Pontiac, etc.):5x100mm, 5x115 mm, 5x120.7&nbsp;mm, 6X139.7&nbsp;mm
+Honda/Acura: 5x114.3&nbsp;mm, 4x100 mm, 4x114.3&nbsp;mm
+Jeep Wrangler JK 07-UP	17"&18"	5x127mm	5x5in
+Mazda: 5x114.3&nbsp;mm, 4x110 mm, 4x114.3 mm
+Nissan/Infiniti: 5x114.3&nbsp;mm, 4x114.3&nbsp;mm
+Peugeot/Citroen: 4x108mm
+Porsche: 5x130mm
+Renault: 5x108 mm, 4x100 mm
+Volvo/Jaguar: 5x108mm
+Subaru: 5x100mm, 5x114.3mm
+Toyota/Lexus/Scion: 5x114.3&nbsp;mm, 5x100 mm, 4x114.3 mm
+VW/Seat/Audi:5x100mm, 5x112 mm
+This guide is accurate for most of the cars made by the listed manufacturers, but it is important to check and make sure before purchasing new aftermarket wheels.
+The BCD may be expressed in millimeters or inches, and is usually given with the number of bolts.  For example, a 1974 [[MG B]] has a 4/4.5&nbsp;inch (4/114.3&nbsp;mm) wheel hub, meaning it has a 4-bolt pattern with a 4.5&nbsp;inch (114.3&nbsp;mm) bolt circle diameter.
+The most common BCD values are 100&nbsp;mm (≈3.94&nbsp;inches) and 4.5&nbsp;inches (114.3&nbsp;mm). Many old British cars use 4 x 4"
+Special BCD values are: 95.25&nbsp;mm (for [[MG F / MG TF|MG F]] and [[Rover Metro]]), 98&nbsp;mm (for [[Fiat]] group automobiles), 101.6&nbsp;mm (for Mini, MG, [[Austin Metro]]), 100 or 105&nbsp;mm (for some GM vehicles), 108&nbsp;mm (mostly for PSA, Ford and [[Lincoln Motor Company|Lincoln]]), 110&nbsp;mm (for some GM vehicles), 112&nbsp;mm (for [[Mercedes-Benz]] and some VW group vehicles), 115&nbsp;mm (for some GM vehicles), 120&nbsp;mm (mostly for BMW), 130&nbsp;mm (for Porsche), 170&nbsp;mm (for [[Saab 96]]). Old British [[Triumph Motor Company|Triumph]] cars used 4 x 3.75" using 3/8" studs. (7/16" or M12 studs are advisable for track use)
+===Determining the bolt circle===
+For a 4- or 6-bolt wheel, this measurement is merely the distance between the center of two [[diametrically opposite]] bolts. In the 4-bolt picture above, this would be the distance between holes #1 and #4, for example.
+Some basic geometry is needed to find the center of a 5-bolt pattern. In practice, the BCD can be found by multiplying the center distance between any two adjacent holes by 1.701.
+:{| class="toccolours collapsible collapsed" width="60%" style="text-align:left"
+!BCD geometry of 5-bolt pattern
+|-
+|
+:<math>\sin\left(\text{half top angle}\right) = \frac {\text{center distance}} {2 \times \text{radius}}</math>
+or
+:<math>\text{radius} = \frac {\text{center distance}} {2 \times \sin\left(\text{half top angle}\right)}</math>
+half the top angle of a 5-bolt wheel is:
+:<math>\frac{360^{\circ}}{5} \times \frac{1}{2} = 36^{\circ}</math>
+using a [[1 (number)|unity center distance of 1]], a bolt circle diameter = 2 × radius, and sin(36) = 0.58778:
+:<math>{BCD} = 2 \times \frac {1} {2 \times 0.58778} = 1.701</math>
+|}
+Generally, the BCD ''b'' can be calculated for any wheel from the number of bolts ''n'' and the [[center distance]] ''d'' between two adjacent bolts as: <math>b = \frac{d}{\sin \left( \frac{1}{n}180^{\circ} \right) }</math>.
+A far easier way, using less math, is to take calipers and measure the hole size in the center of the wheel (note half of this dimension). Next measure the distance between the edge of the center hole and the center of one stud.  Double this measurement and add it to the Noted sum. Job done!  (That is determine the radius of the hole size, not the diameter) This method works with any number of studs.
+==Lug nuts or bolts==
+Wheels must be fitted with the correct type of [[lug nut]]s on [[wheel stud]]s, or bolts. Lug nuts (aka wheel nuts in British English) are usually either flat, tapered (generally at 60 degrees and referred to as conical seat), or ball seats, meaning the mounting surfaces are flat, tapered, or spherical respectively.
+Most [[Mercedes-Benz|Mercedes]] have ball lug seats from the factory while most aftermarket wheels have a tapered lug design. Wrong lug nuts for the wheel will not properly center it and cause wobble. Some manufacturers (e.g. [[Toyota]] and [[Lexus]]) have used taper lug nuts for steel wheels and flat seated lug nuts for [[alloy wheel]]s.
+Some aftermarket wheels will only fit smaller lug nuts, or not allow an ordinary lug nut to be [[Torque wrench|properly torqued down]] because a socket will not fit into the lug hole. Tuner lug nuts were created to solve this problem by utilizing a special key to allow removal and installation with standard lug wrench or socket. The design of tuner lug nuts can range from bit style to multisided or spline drive, and are sometimes lightweight for performance purposes.
+A variation is the "locking wheel nut", which is almost universally used for alloy wheels in the United Kingdom. One standard lug nut on each wheel is replaced with a nut which requires a special and unique key (typically a computer-designed, rounded star shape) to fit and remove the nut. This helps to discourage theft of wheels. However, universal removal tools are available which grip the head of the locking nut using a hardened left-hand thread. The success of these depends on whether there is room to use it in the lug hole, and whether the manufacturer has incorporated a free-spinning outer casing to the lock. Keeping an appropriate tool to lock and unlock aftermarket nuts, and a spare set of nuts, with the spare tire in the boot of the car is recommended by manufacturers.
+==Centerbore==
+The centerbore of a wheel is the size of the hole in the back of the wheel that centers it over the mounting hub of the car. Some factory wheels have a centerbore that matches exactly with the hub to reduce vibration by keeping the wheel centered. Wheels with the correct centerbore to the car they will be mounted on are known as hubcentric. Hubcentric wheels take the stress off the lug nuts, reducing the job of the lug nuts to center the wheel to the car. Wheels that are not hubcentric are known as lugcentric, as the job of centering is done by the lug nuts assuming they are properly torqued down.
+Centerbore on aftermarket wheels must be equal to or greater than that of the hub, otherwise the wheel cannot be mounted on the car. Many aftermarket wheels come with "hubcentric rings" that lock or slide into the back of the wheel to adapt a wheel with a larger centerbore to a smaller hub.<ref>{{cite web|title=Hubcentric-rings.com|work=Why hub centric rings?|url=http://www.hubcentric-rings.com/miksi_soviterengas/|accessdate=21 Mar 2011}}</ref>  These adapters are usually made of plastic but also in aluminum.
+==X-factor==
+Caliper Clearance (X-factor): The amount of clearance built into the wheel to allow for the vehicle's [[disc brake]] and caliper assembly.
+==Load capacity==
+Load capacity is the amount of weight a wheel will carry. This number will vary depending on the number of lugs, the PCD, the material used and the type of axle the wheel is used on. A wheel used on a free rolling trailer axle will carry more weight than that same wheel used on the drive or steering axle of a vehicle. All wheels will have the load capacity stamped on the back of the wheel.
+==GVWR==
+This is the [[Gross Vehicle Weight Rating]]. In the United States this information is required to be on the vehicle's door placard. The load capacity of the total number of wheels on the vehicle combined must meet or exceed the vehicle's GVWR.
+==References==
+{{Reflist}}
+==See also==
+* [[Plus sizing]]
+* [[Speedometer#Error]] - handy tire diameter formula, using [[tire code]]
+{{DEFAULTSORT:Wheel Sizing}}
+[[Category:Automotive technologies]]
+[[Category:Mechanical standards]]

Bijective proof: Difference between revisions

Latest revision as of 23:15, 19 March 2013

Contents

Bolt pattern

Bolt circle

Determining the bolt circle

Lug nuts or bolts

Centerbore

X-factor

Load capacity

GVWR

References

See also

Navigation menu

Bijective proof: Difference between revisions

Latest revision as of 23:15, 19 March 2013

Bolt pattern

Bolt circle

Determining the bolt circle

Lug nuts or bolts

Centerbore

X-factor

Load capacity

GVWR

References

See also

Navigation menu

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