Tire

Tire, an homonymous word, of which the meanings are (1) to weary out, (2) to adorn, or, as a substantive, a head-dress, (3) the outer rim of a wheel. " Tire " in sense (1) is from the Old English teorian, to weary, transitive and intransitive. Ultimately this word is connected with" tear," to rend, the stages of meaning being to rend apart, to wear out, to be or make exhausted.

In sense (2) the word is a shortened form of " attire," dress, equipment; this is from the Old French atirer, to put in order, tire, a row, hence the word now spelled in English tier, but earlier found as tire or tyre. " Tire " (3) is somewhat obscure etymologically. It may be connected with " attire," especially with reference to a similarity to the band of a woman's headdress, or it may be a corruption of " tie-r," meaning that which " ties " or fastens together, though this is rejected by Skeat. The spelling " tyre " is not now accepted by the best English authorities, and is unrecognized in America.

The tire of a wheel is the outer circumferential portion that rolls on the ground or the track prepared for it. When the track is smooth and level, as in a railway, the principal functions of the tire are to provide a hard, durable surface for the wheel, and to reduce to a minimum the resistance to rolling. Railway vehicle wheels usually have hard steel tires, this combination with the hard steel rail giving the maximum endurance and the minimum rolling resistance. For road vehicles also, in which durability is the prime consideration, the tires are usually rings of iron or steel shrunk on the wooden wheels.

In bicycles, motor-cars, and other road vehicles in which freedom from vibration and shock from uneven road surface is desired, rubber or pneumatic tires are employed. These elastic tires are capable of absorbing small irregularities in the road surface without transmitting much vibration to the frame of the vehicle. Their range of yield is, however, too limited to absorb the larger irregularities met with on rough roads, so that their use does not obviate the necessity of spring support of the carriage body on the wheel axles. The pneumatic tire has a very much smaller rolling resistance than a solid rubber tire. Where the driving power is limited, as in bicycles, this consideration is by far the most important. A pneumatic tired bicycle requires less power to drive it at a given speed than does one with solid rubber tires - in popular language, it is much faster; hence pneumatic tires are now almost universally used on bicycles.

## Rolling Resistance

Professor Osborne Reynolds, in his investi gations on the nature of rolling resistance, found that it is due to actual sliding of the surfaces in contact. Fig. I shows an iron roller C f resting on a flat, thick sheet of india-rubber. A series of equidis tant parallel lines drawn on the india-rubber are distorted by the FIG. I. pressure, as shown in the figure.

The distance between the marks on the periphery of the roller corresponds to that between the lines on the undistorted sheet of rubber. The motion of the roller being from left to right, actual contact takes place between C and D. The surface of the rubber is depressed at P, is bulged up in front at D, and behind at C. The vertical compression of the rubber at P causes it to bulge laterally, this causing a lateral contraction at D, which in turn causes a vertical extension at D.  There is thus created a tendency to relative creeping motion between the roller and rubber. Between f and e there is no relative sliding, but over the portions eD and Cf there is slipping, with a consequent expenditure of energy. The action causes the actual distance traversed by the roller to be different from the geometric distance calculated from the diameter and number of revolutions of the roller. A certain amount of energy is expended in distorting the rubber between P and D; part of this energy is restored as the rear portion of the roller passes over this and the rubber gets back to its original unstrained state.

With a solid rubber tire rolling on a hard, smooth surface the action is similar. Fig. 2 shows a portion of the tire flattened out: vs pi and p2 are the intensities of the pressures at points a i and a 2 at equal distances in front of and behind c, the geometrical point of contact: p i opposes, p 2 assists the P d P, rolling of the wheel. At usual.

speeds the opposing force, pi, will FIG. 2. be greater than the force of resti tution, p 21 the difference being a measure of the elastic hysteresis of the material, H, at that speed. If the vertical compression cd of the tire be denoted by y, the energy lost may be said to be proportional to Hy. Comparing three tires of steel, solid rubber and air respectively rolling on a smooth, hard surface, H is probably smallest for steel and largest for rubber, y is least for steel, greater for a pneumatic tire pumped hard, greater still for solid rubber and for a pneumatic tire insufficiently inflated. The rolling resistance of the steel tire will therefore be least; next in order come the pneumatic tire inflated hard, and the pneumatic tire inflated soft, while the solid rubber tire has the greatest resistance.

## Pneumatic Tires. Weight Supported

Let a pneumatic tire inflated to p lb per square inch support a load W lb. The portion q FIG. 3.

near the ground is flattened (fig. 3). If the tire fabric is assumed to be perfectly flexible, then, since the part in contact with the ground is quite flat, the pressure p and q on the opposite sides must be equal; that is, the tire presses on the ground with an intensity p lb per square inch. The area of the flattened portion FIG. 4.

is therefore W/p. Fig. 4 shows the shapes of the areas of contact of a bicycle tire 28 in. by I z in., for various amounts of vertical flattening, the figures annexed to the curves in plan and to the corresponding lines in elevation indicating the amount of vertical flattening in sixteenth parts of an inch. Let y be the vertical flattening, a the semi-major axis, and b the semi-minor axis of the curve of contact. For small values of y, corresponding to a tire pumped hard, the curves of contact may be considered plane sections of a circular ring. The area of the curve may be taken equal to that of an ellipse having the same axes, i.e. 7rab. But a= R 2 - (R - y) 2 =-12Ry - y 2 = y 1,12R - y, and b= AIr2 - (r_y)2= J 112r - y, R and r being the principal radii of section of the tire longitudinally and transversely. Therefore, approximately, A =7rab =7ry V2R - yJ2r - y.  For small values of y, y may be neglected in comparison with 2R and zr respectively, and the above equation becomes A =27ry ,/Rr Dd, and therefore W = 27rypAIRr =7rypiiDd.  For larger values of y, A is smaller than that given by the above formula, as shown in fig. 5, which gives the areas of contact plotted with respect to the vertical flattenings for a tire 28 in. by I I in. The same curve may serve to show values of W, thus corresponding to the load-deflection curve of a spring. The - 5 curve clearly shows the small value of the pneumatic tire as a spring device. Thus, when pumped hard, so that the normal load is carried with in. vertical flattening, when the bicycle is travelling quickly, a lump on i ai "1. the road equivalent to s in. further flattening nearly doubles the upward reaction on the FIG. 5. wheel. With the normal load carried with in. vertical flattening the same lump on the road increases the upward reaction by only 23%, the area of contact of the tire being d b c, c; b FIG. 6.

increased from 6.5 to 8 sq. in. The above brief investigation, involving a few approximations, is yet sufficiently accurate to afford a clear idea of the usual conditions of a tire.

  


## Outer Cover

The outer cover has to be strong enough to withstand the air-pressure inside the tire and to transmit the driving or the braking effort from the wheel to the road surface. For the latter purpose, the threads of the fabric are best disposed spirally, as shown in fig. 6. While driving in the direction of the arrow the tension on the fibres cc will be slightly increased, that on fibres dd  decreased. The distortion of the fabric due to driving is thus reduced to a minimum. A woven fabric is sometimes used, but one made up of two or more layers of parallel threads embedded in rubber is better. This construction makes the outer cover more flexible, and consequently less energy is wasted in distorting the fabric as the tire rolls on and off the ground, while greater durability is also secured. Fig. 7 shows a plain woven fabric, from which it is seen that each thread takes the form of a sinuous line. As the air-pressure inside the tire is increased the threads tend to become straighter, thus pressing together with a cutting action. The total thickness is greater than that of two layers of parallel threads, while on the latter the threads can be placed closer together. The woven fabric is therefore stiffer, weaker and less durable than that built up of parallel layers. The average 7. tensile stress per inch width, t 1 , on the FIG.

longitudinal section of the cover is given by the formula pd=2t 1; that on the transverse section, t2, by pd = 4 t 2 , being the diameter of the tire in transverse section; consequently the stress on the longitudinal section is twice that on the transverse. With the spiral disposition of the threads, as shown in fig. 6, this inequality of stress in the two principal directions has the effect of tending to enlarge the transverse section of the tire, while at the same time tending to contract the tire on the rim.

## Single tube, Double tube and Tubeless Tires

A tire, beside being strong enough to resist the stresses to which it is subjected, must be air-tight. In most tires for cycles and motor-cars an inner tube of india-rubber is made separate from the outer cover. In these doubletube tires the outer cover is more or less easily detachable from the rim. The air under pressure is pumped inside the inner tube, which is supported by the outer cover. In case of puncture of a bicycle tire, the inner tube is repaired by cementing a patch of rubber on the outside of the inner tube, a solution of india-rubber in naphtha or bisulphide of carbon being the cementing agent employed. Motor-car tires are best repaired by vulcanizing, as solution patches usually come loose owing to the heating of the tire. In a single-tube tire, as its name indicates, the outer cover and the air-tight tube are vulcanized together to form a single hollow ring. To repair a simple puncture of a single-tube tire it is not necessary to detach it from the rim. Single-tube tires are not often used now, except for path-racing bicycles. A tubeless tire, such as the " Fleuss " (fig. 8), consists of the outer cover, as used in a double-tube tire, to the inner surface of which an air-tight layer of sheet-rubber has been cemented. A continuous flap projects from one edge of the tire, and when in position on the rim this flap is pressed against the other edge, forming an air-tight seal. A slight moistening of the flap with soft soap tends to remove any imperfection in the tightness of the air seal. The repair of a puncture of a tubeless tire can be very quickly done. Since the inner surface of the airtight layer is accessible, after placing the patch in position the tire can be inflated and the bicycle ridden at once; whereas in the doubletube tire sufficient time must elapse between the patching and the inflation to allow the rubber solution to set.

## Attachment of Tires to Rims

A single-tube tire can be cemented directly to the rim. For detachable double-tube tires on bicycles, two methods, the Dunlop-Welch endless wire (fig. 9) and the " beaded edge " (fig. I I), account for by far the greater proportion. In the Dunlop-Welch tire the endless wires are embedded in the two edges of the outer cover respectively, the transverse tension of the fabric being transmitted to them. Each endless wire is formed of three coils, oUNLOP so as to give flexibility to the edge of the cover. The ring formed by each endless FIG. 9. wire is smaller in diameter than the edge of the rim. The middle portion of the rim is deepened, its diameter being less than that of the ring of endless wire. To detach the tire after deflation, one part of the edge of the outer cover is depressed into the bottom of the rim, the opposite part then projects slightly beyond the edge of the rim and is pulled outside; one portion being got outside, the rest easily follows. Fig. 10 shows the nature of the mutual action between outer cover C, rim R, and endless wire W in a Dunlop-Welch tire. The transverse tension T on the outer cover is transmitted to the endless wire W, which is also subjected to the reaction N of the rim. The resultant Q must lie in the plane of the endless wire W, and constitutes a radially outward force acting at all points, which in turn causes a longitudinal pull, P, on the wire. Let d be the diameter of the inner air-tube, D the diameter of the ring formed by the endless wire W, p the air pressure, and 8 the angle FIG. IO. FIG. I I.

between T and Q. Then for each inch length of wire T = pd/2, Q = T/cos 0; while P = QD/2. Combining these results, we get P =pdD/4 cos 0. If 0 =30°, P=o29pdD, from which the section of wire for a tire of any size can be calculated.

In the " beaded edge " fastening, thickened edges on the outer cover take into corresponding edges formed on the rim, and are securely held therein when the tire is inflated.

## Prevention of Punctures

The outside of the tire is covered with a thick layer of rubber, which protects the fabric from injury by contact with the rough road surfaces. In full roadster tires this outer layer of rubber is thinner at the sides than at the tread (the part which actually rolls on the ground), but still completely covers the fabric. In light roadster and racing tires the sides are not covered, and an appreciable gain in speed or ease of driving is due to the greater flexibility of the cover thus obtained. Numerous puncture-proof bands and other devices have been tried with the object of absolutely preventing punctures, or making the tire selfsealing after puncture; but they increase the rolling resistance, and therefore the effort necessary to drive the bicycle at a given speed.

## Valve for Pneumatic Tire

A non-return valve is permanently attached to the inner tube of the tire, which allows the air forced from the inflater to pass inside the inner tube. The most commonly used, the Dunlop-Woods valve, consists of a short piece of rubber tubing mounted on a brass stem, which has a small hole communicating from its outer end to the inner surface of the rubber tube. Normally, the tubing closes the mouth of this hole, preventing the air from escaping from the tire, but lifts freely when air is being forced from the inflater. The arrangement of the parts for deflating and for getting access to the rubber tubing is very simple and effective. The cyclist should be careful that the small piece of valve tubing, and the two fibre washers at the ends of the flexible connecter which serve to make air-tight the two joints between the latter and the pump and valve stem respectively, are always in good condition. If either of these seemingly small details is out of order it may be impossible to pump the tires hard enough; the bicycle being ridden, the tires may be nipped in many places between the rim and sharp edges on the road surface, and practically ruined.

Tires for Motor Cars. - In the cost of upkeep of a motor car the tires are the most expensive item. For a slow speed vehicle an ordinary steel tire, shrunk or hydraulically pressed on a wooden wheel, is cheap and durable. At higher speeds over uneven roads it is less satisfactory; the wheel, forming with the tire one rigid body, receives violent accelerations vertically, due to the uneven road, and is being continually shot upwards into the air out of contact with the ground. Thus excessive noise and vibration are caused at all but very moderate speeds, and for passenger cars an elastic tire is a necessity. The solid rubber tire, not being liable to puncture, is trustworthy if made of sufficient sectional area, but it is expensive and lacks the comfort and easy running of the pneumatic. The motor car pneumatic tire is made on the same lines as the cycle tire, but the air-tube is thicker, and the outer cover is built up with FIG. 12.

several layers of canvas or fabric to give the necessary strength (fig. 14). To provide for wear, the outer protective layer of rubber is considerably thickened at the tread, where it is also reinforced with two or three layers of canvas. The Palmer cord tire is built up of two layers of cord (fig. 12) arranged spirally, each cord being composed of four strands of six threads. The cords are flattened FIG. 8.

somewhat, their narrow surfaces being together at the tread of the tire, and their wide ones at the beaded edge. The anchorage of the cord to the beaded edge is obtained by steel pins passing through the loops of the cord and into the canvas beads (fig. 13). The cords, tread and beads being all vulcanized together, the tire is practically impervious to moisture, and has therefore less tendency to rot than a canvas tire. Further, the threads, by the process of manufacture, are insulated each from the others by a layer of rubber, and there is thus less tendency for them to fray or saw each other as the tire yields during continuous running. These features of construction tend to greater durability.

## Strains on Fabric of Pneumatic Tire

As each portion of the tread comes in contact with the ground it is flattened, while the rest of the transverse section has its radius of curvature slightly decreased (fig. 3). Thus the transverse section is repeatedly undergoing flexure through a range extending from flatness (radius of curvature infinity) to a radius of curvature slightly less than that of the normal section. On the longitudinal section the range of flexure is from flat to a radius of curvature equal to that of the normal section. The latter range is therefore much less than the former. The necessary thickness of the fabric and rubber to resist the air pressure and punctures involves a certain amount of stiffness; consequently the energy expended in the flexure of the tire is much greater than in a thin cycle tire. This energy appears as heat; the temperature of the cover rises until the heat carried away by the air is equal to that generated by flexure. At very high speeds this heating becomes so great as to have fan injurious action on the rubber and fabric. Unfortunately, the solid rubber tire is worse off in this respect, its elastic hysteresis, and therefore the heating effect, being greater than that of a pneumatic tire. It is evident that increase of the diameter of the tire-section lessens the heating action, while reduction of diameter of the wheel has no effect, so long as the range of longitudinal flexure is less than the transverse. Nearly all tire fabrics are equally stiff longitudinally and transversely; but probably greater durability would be obtained from a fabric more flexible transversely, even if somewhat stiffer longitudinally.

## Pneumatic Tires for Heavy Loads

From the formula for load supported, W = iryp-sl Dd, for a given air pressure p and vertical flattening y, the load supported is proportional to the square root of the product of the longitudinal and transverse diameters; thus a tire 36" X4" is equivalent to one 24" X6". But the latter can be subjected to a much greater vertical flattening y than the former, with a less range of flexure of the cover, probably twice the amount. In this event, with the same air pressures, the 24"X6" tire could carry a load twice that of the 36" X4" tire. Or, if both tires carried the same load, the air pressure in the former might be half that in the latter, and, its vertical flattening under normal load being twice as great, its value as a spring in absorbing vertical unevenness of the road would be double. Since the first use of pneumatic tires for motor cars, they have been steadily reduced in diameter, and probably they can be made still smaller with advantage, if the transverse section be proportionately increased.

The following table gives the maximum loads and minimum air pressures for a few sizes of tires, as recommended by the Dunlop Pneumatic Tire Company. The corresponding vertical flattening has been calculated from the formula given above.

| 

Diameter.

| 

Section.

| 

Maximum

Load per

| 

Minimum

Air

Pressure.

| 

Vertical

Flattening.

g'  
  
---|---|---|---|---|---  
| 

In.

| 

In.

| 

lb

| 

lb

per sq. in.

| 

In.  
  
Light

| 

28

| 

21

| 

360

| 

70

| 

19  
  
Car

| 

28

| 

3

| 

400

| 

75

| 

19  
  
Tires

| 

28

| 

32

| 

700

| 

80

| 

25  
  
Heavy

| 

' 32

| 

31

| 

900

| 

80

| 

.33  
  
Car

| 

32

| 

4

| 

1000

| 

85

| 

33  
  
Tires

| 

32

| 

5

| 

1300

| 

95

| 

'34  
  
## Fastenings of Motor Tires to Rims

The  beaded edge " type of fastening is most largely used, supplemented by security bolts (fig. 14). Fig. 13 shows a flange fastening as used for the Palmer cord tire, the two flanges being secured by a number of bolts passing through the rim of the wheel.

## Solid Rubber Tires for Heavy Vehicles

Fig. 15 shows a section of a solid rubber tire and rim, the rubber being forced under pressure on the beaded rim. For very heavy loads, as in motor omnibuses, a twin tire gives the best results. The two tires are fastened on the same rim, at a sufficient distance apart to allow each to bulge laterally as it rolls on the ground.

FIG. 14. FIG. 15.

## Non-Skid Devices

As a pneumatic tire flattens where it is in contact with the road, under certain conditions of road surface a semi-liquid film of mud gets interposed, and frictional contact is reduced to a minimum. The vehicle has then no lateral constraint, and side-slipping or skidding may occur. On a bicycle this means a dismount, probably a severe fall; on a three or four-wheeled vehicle the steering control is temporarily lost. Cycle tires are usually provided with longitudinal ridges at the tread (figs. 8, 9, I I); the narrow surfaces of the ridges penetrate the mud and get a better grip on the solid road surface. Motor car tires are sometimes left with a smooth tread (fig. 14); fig. 13 shows a non-slipping tread with longitudinal ridges. The Dunlop non-slipping tread is formed by a series of lateral grooves about 2 in. apart all round the tread. Fig. 16 shows a tire fitted with a non-skid leather band, to which hard steel studs are fastened. This type of non-skid band can be either vulcanized to the tire or independently fastened to the rim at the beaded edges. The Parsons " non-skid " device consists of chains crossing the tire at right angles and fitting loosely over its surface; they are fastened at intervals to two chain rings one on each side of the wheel, and can be easily adapted to any tire. (A. SP.)