Agricultural Engineering · Farm Machinery & Power · also Soil Dynamics in Tillage and Traction, Tractor Mechanics
How soil resists tools and supports wheels: draft, slip, tractive efficiency, weight transfer and stability.
In the exams: GATE AG Section 3 (traction asked in all 8 papers 2019–26; weight transfer and stability in 5 of 8); ICAR AICE subject 39 Unit 6; ASRB NET FMP
Soil dynamics in tillage and traction is the mechanics of soil when a machine acts on it: when a tine, disc or mouldboard cuts and moves it, and when a wheel or track pushes against it to move a vehicle. The first half of the subject asks how much force an implement needs and why that force changes with soil, depth, speed and tool shape. The second half asks how a tractor turns engine power into pull through slipping, sinking tyres, how pulling moves weight from the front axle to the rear, and when that transfer, a slope or a turn tips the tractor over. The subject connects soil mechanics, which gives the strength parameters, to farm power and machinery, which gives the machines.
It matters in practice because most of a tractor's fuel in primary tillage is spent at the soil: in cutting and lifting soil, in tyres slipping, and in wheels rolling through ruts they make themselves. A tractor that is badly ballasted, on the wrong tyre pressure or matched to an implement too wide for it wastes fuel, compacts the subsoil and, in the worst case, overturns. Tractor overturns are among the leading causes of death in farm work in many countries, and weight transfer and stability are the mechanics behind them.
Exams everywhere treat this as a calculation subject. In India, GATE Agricultural Engineering regularly asks traction questions (slip, rolling radius, tractive efficiency, net traction, maximum thrust on sand), and weight transfer or stability questions often appear as well. ICAR AICE-JRF/SRF lists soil dynamics in tillage and traction as a unit of Farm Machinery and Power Engineering, and ASRB NET includes it under Farm Machinery and Power. The US PE Agricultural and Biological Engineering exam supplies ASABE machinery management standards and expects candidates to use their draft and traction relationships; the Philippine licensure exam covers the same ground under power and machinery. This manual gives the theory, the standard equations, worked reasoning and the judgement a practitioner needs. Where a value depends on soil, tyre or country, it says so rather than quoting one number.
Soil dynamics is the study of soil in motion under a tool or traction device. Gill and Vanden Berg, in the classic US Department of Agriculture handbook Soil Dynamics in Tillage and Traction, separated the properties that matter into two groups. Condition properties describe the state of the soil at the moment of loading: moisture content, bulk density (dry mass per unit total volume), porosity, structure and texture. Dynamic properties are the soil's responses when it is loaded: shear strength, compressibility, soil-metal friction, adhesion (soil sticking to a surface), plasticity and the resistance to penetration. The same field can behave like a friable crumb in the morning and a sticky paste after rain, because the condition properties have changed and every dynamic property follows. That is why the draft of a plough or the pull of a tractor is never a fixed number for a 'soil type'; it is a number for a soil type in a particular condition. Texture (the proportion of sand, silt and clay) sets the range; moisture and density decide where in the range the soil sits on a given day. Engineers therefore report draft and traction data together with the moisture content, bulk density or cone index at which they were measured.
Soil fails in shear. The Mohr-Coulomb law states that the shear stress τ at failure on a plane equals c + σ tan φ, where c is cohesion (the part of strength that does not depend on normal stress), σ is the normal stress on the failure plane and φ is the angle of internal friction. Dry sand has c close to zero and φ typically in the range of about 30 to 40 degrees depending on density and grading; a clay at moderate moisture has appreciable cohesion and a lower φ. The parameters are measured in the laboratory with the direct shear box or the triaxial test, and in the field with the shear vane, the annular (ring) shear device or the bevameter, which combines a sinkage plate with a shear ring to measure the parameters a vehicle actually meets. For the fast loading under a tool or a tyre, the soil has little time to drain, so strength measured quickly in the field often matches machine behaviour better than drained laboratory values. Strength rises with bulk density and, for cohesive soils, falls steeply as moisture rises beyond the plastic limit. The Atterberg limits (liquid limit, plastic limit and the plasticity index between them) therefore tell the engineer when a clay soil will crumble, smear or flow under a tool.
Where soil slides on a tool or a tyre, a second, weaker strength law applies: the soil-to-surface shear stress equals ca + σ tan δ, where ca is adhesion and δ is the angle of soil-metal (or soil-rubber) friction. δ is normally smaller than φ, because sliding on a smooth surface is easier than shearing soil against soil; if a surface is rough enough that soil sticks to it, failure moves into the soil and φ governs instead. Adhesion rises with clay content and with moisture up to a point, then falls again as a water film lubricates the interface. Scouring, the ability of a mouldboard to shed soil cleanly, depends on this balance: when adhesion is high, soil builds up on the tool, the effective shape changes and draft rises. Designers counter it with polished hardened steel, low-friction coatings or plastic facings, and by changing the tool angle. Soil-metal friction is also the reason abrasive sandy soils wear shares fast, while sticky clays cause build-up rather than wear.
A tool moving through soil pushes a wedge of soil ahead of it until the soil shears along a failure surface running forward and up to the ground. The soil then fails in one of three broad ways. In brittle or friable soil it breaks into blocks or chips that ride up the tool (block and chip failure). In wetter plastic soil it deforms continuously and flows over the tool (flow failure). Between these, soil may shear in successive slices, so the draft force rises and falls in a saw-tooth pattern as each block forms and breaks away. The failure surface of a wide blade in cohesive soil is often approximated by a log-spiral or a straight line, which lets the passive earth-pressure theory of retaining walls be used: the tool is a wall pushed into the soil, and the soil resists with passive pressure. Tool geometry changes the failure. The rake angle is the angle of the tool face measured from the horizontal in the direction of travel; a small rake angle lifts soil gently and needs less draft, while a steep rake angle pushes soil forward, increases draft and increases the downward or upward vertical force.
A narrow tine, whose depth is several times its width, does not behave like a wide blade. Godwin and Spoor showed that near the surface soil fails upward and forward in a crescent shape, loosening a wedge wider than the tine. Below a certain depth, called the critical depth, the soil can no longer be lifted to the surface; it moves sideways around the tine and is compacted rather than loosened. Critical depth increases with tool width and decreases as rake angle increases; it also depends on soil moisture and density. Working a subsoiler below its critical depth is a classic mistake: draft rises, the soil below is smeared and compacted, and little loosening is achieved. Practical remedies are to fit wings to the foot of the tine, to reduce the rake angle, or to use shallow leading tines that loosen the upper layer first so that the deep tine's critical depth is effectively lowered. The same idea explains why cultivators with staggered tines at close spacing loosen the whole width, while widely spaced tines leave untilled ridges between them.
Reece adapted Terzaghi's bearing-capacity form to tools, giving what is often called the universal earthmoving equation. The force on a wide tool is F = (γ d² Nγ + c d Nc + ca d Nca + q d Nq) w, where γ is the soil unit weight, d the working depth, c cohesion, ca adhesion, q a surcharge pressure on the soil surface, w the tool width, and the N terms are dimensionless factors that depend on φ, δ, rake angle and the depth-to-width ratio. The first term is the weight of soil lifted; the second and third are the cohesive and adhesive resistance; the fourth is surcharge. The equation shows two useful scalings: the gravity term rises with the square of depth while the cohesion term rises with depth, so in cohesive soil draft rises roughly in proportion to depth and in cohesionless soil more steeply. Speed adds an inertial term, because soil must be accelerated; draft of most tillage tools rises with speed, roughly linearly at low speeds and more steeply at high speed. For narrow tines the equation is corrected for the side (three-dimensional) failure, which adds force beyond the width of the tool.
The resultant soil force on a tool has three components: the horizontal component along the direction of travel (draft), the vertical component (suction or lift) and the lateral or side component. A plough mouldboard throws soil to one side, so it has a side force that is resisted by the landside and the rear furrow wheel. Disc implements have large side and vertical forces; a disc plough relies on its own weight to penetrate, while a disc harrow's gangs are set at opposing angles so their side forces largely cancel. The resultant acts at the centre of resistance of the implement, and the line of pull from the tractor hitch should pass through it for the implement to run true without side draft. Wear changes all of this: a blunt share with a worn point loses suction, rides out of the ground and needs extra weight or depth-control effort. For a trailed implement the vertical component of the soil force and the implement weight are carried by its own wheels; for a mounted implement they are passed through the linkage to the tractor, which is the link to weight transfer in a later chapter.
Draft is the horizontal force parallel to the line of travel needed to pull an implement. Because the full theory needs parameters rarely measured on farms, practitioners predict draft from empirical relationships. The simplest is unit draft: draft per unit width (for harrows, cultivators and seed drills, in newtons or kilonewtons per metre, or per row for planters) or draft per unit cross-sectional area of the furrow for ploughs, called the specific soil resistance or specific draft. For a mouldboard plough, draft equals specific resistance times the number of bottoms times the width per bottom times depth. Specific resistance varies by several times from light sandy soils to heavy clays, and within one soil with moisture and speed, so any value from a table is a starting estimate. Exam problems give the value; practice requires measured or local data. Always keep units consistent: a specific resistance in kilopascals times an area in square metres gives kilonewtons; a common slip is to leave furrow dimensions in centimetres.
ASABE Standard D497, Agricultural Machinery Management Data, gives a general equation for implement draft: D = Fi [A + B S + C S²] W T, where D is draft in newtons, Fi is a dimensionless soil texture adjustment factor with i = 1 for fine, 2 for medium and 3 for coarse textured soils, A, B and C are machine-specific parameters, S is field speed in km/h, W is machine width in metres (or number of rows or tools) and T is tillage depth in centimetres (T is taken as 1 for minor tillage tools and seeding implements). The S² term carries the speed effect for implements that accelerate soil strongly, such as mouldboard ploughs; for many tools B and C are small or zero. The standard also gives an expected range, often plus or minus a large percentage, which reminds the user how variable draft is. The PE Agricultural and Biological Engineering exam supplies this standard; the skill tested is choosing the right row of the table, the right texture factor and keeping S, W and T in the stated units.
Drawbar power is draft times travel speed: P (kW) = D (kN) × v (m/s), or D (kN) × v (km/h) / 3.6. It is the power the implement needs at the hitch, not the power the engine must produce. To get engine or PTO power, divide by the efficiency of every link: tractive efficiency (the tyres), transmission efficiency and any allowance for the fraction of rated power the engine should run at. A mounted rotary implement driven by the PTO also has a PTO power demand, and its draft may even be negative because the rotor pushes the tractor forward. Field capacity links draft to management: a wider implement covers more hectares per hour but multiplies the draft, and the tractor must supply it at a slip level that keeps tractive efficiency high. Matching a tractor to an implement is therefore a traction calculation, not just a comparison of engine rating and implement width.
A driven wheel receives an axle torque T from the tractor. If the wheel has an effective radius r, the torque corresponds to a gross traction or gross thrust GT = T / r, the force the tyre would produce on the soil if nothing were lost. Part of that force is used to overcome motion resistance, also called rolling resistance (RR): the force needed to roll the wheel, arising mostly from soil deformation (the rut it makes), plus tyre flexing. What is left is net traction NT, also called drawbar pull: NT = GT − RR. Dividing each force by the dynamic load on the wheel W gives dimensionless ratios: gross traction ratio GTR = GT/W, motion resistance ratio MRR = RR/W and net traction ratio NTR = NT/W, sometimes called the coefficient of traction. A towed (undriven) wheel has no gross traction, so it needs a pull equal to its rolling resistance; the ratio RR/W is then called the coefficient of rolling resistance. On firm, dry roads this coefficient is small; on soft or freshly tilled soil it is several times larger, which is why a tractor can lose much of its pull just rolling.
A driven wheel on soil moves forward less than its circumference per revolution, because the soil under the lugs shears backwards. Wheel slip (travel reduction) is s = 1 − va/vt, where va is actual forward speed and vt is theoretical speed. The theoretical speed is vt = ω r = 2π N r / 60 for N rev/min, using the rolling radius r. Equivalently, if the wheel makes N0 revolutions over a distance in the reference (no-load) condition and N1 revolutions over the same distance under load, s = 1 − N0/N1; or if in a fixed number of revolutions it travels L0 without load and L1 with load, s = 1 − L1/L0. The rolling radius is the distance travelled per revolution divided by 2π in the reference condition. The choice of reference matters: common choices are the wheel self-propelled at zero net pull on the same surface, or on a hard surface. A negative slip (skid) occurs on towed or braking wheels, when the wheel travels farther than its rolling circumference. Students often invert the ratio, writing (N1 − N0)/N0 instead of (N1 − N0)/N1, which overstates slip.
The maximum thrust a soil can give a traction device is limited by the soil's shear strength over the contact area. Micklethwaite's expression is Hmax = A c + W tan φ, where A is the contact area, c cohesion, W the vertical load and φ the angle of internal friction. Two consequences follow. In dry sand (c = 0), Hmax = W tan φ: thrust depends only on load, not on tyre size, so extra ballast helps but a larger tyre does not. In a purely cohesive saturated clay (φ close to 0), Hmax = A c: thrust depends on contact area, so wider tyres, dual wheels or tracks help while extra weight mainly causes sinkage. Janosi and Hanamoto described how thrust builds with slip: shear stress τ = (c + p tan φ)(1 − e^(−j/K)), where j is shear displacement (which grows with slip and along the contact length) and K is a shear deformation modulus. Bekker's pressure-sinkage relationship, p = (kc/b + kφ) zⁿ, with b the smaller contact dimension, z sinkage and kc, kφ and n soil constants, gives the sinkage and hence the compaction resistance. These terramechanics relationships, developed further by Wong, underlie the physics; the empirical mobility-number equations of the next chapter are what most field engineers use.
Because soil parameters for terramechanics are hard to measure, the US Waterways Experiment Station and later Wismer and Luth used the cone index CI, a single field measurement, to build dimensionless wheel numerics. Wismer and Luth's wheel numeric is Cn = CI b d / W, where b is tyre section width and d is unloaded tyre diameter. Their equations give motion resistance ratio 1.2/Cn + 0.04 and net traction ratio 0.75 (1 − e^(−0.3 Cn s)) − (1.2/Cn + 0.04). Brixius added tyre deflection δ and section height h to form the mobility number Bn = (CI b d / W) × (1 + 5δ/h) / (1 + 3b/d). ASABE D497 adopts Brixius's equations for bias-ply tyres: GTR = 0.88 (1 − e^(−0.1 Bn)) (1 − e^(−7.5 s)) + 0.04 and MRR = 1/Bn + 0.04 + 0.5 s / √Bn, with NTR = GTR − MRR. A high Bn means firm soil or a lightly loaded large tyre; a low Bn means soft soil or an overloaded small tyre. The equations are empirical fits to test data and should be used within the range of tyres and soils they came from.
Tractive efficiency (TE) is the ratio of drawbar power to the power delivered to the driving axles: TE = (NT × va) / (T × ω). Because T ω = GT × vt, this can be written TE = (NT/GT) × (va/vt) = (NT/GT)(1 − s). The expression shows the two losses of a traction device. The first, NT/GT, is the force loss: part of the thrust is used to overcome motion resistance. The second, 1 − s, is the speed loss: slip means the axle turns without advancing the tractor. Equivalently, using ratios, TE = (1 − s) × NTR / (NTR + MRR). Some texts use the reverse ratio, axle power over drawbar power; exam questions always define which they mean, and a value above one signals the inverted definition. Tractive efficiency is distinct from drawbar efficiency or power delivery efficiency, which is drawbar power divided by engine or PTO power and so includes transmission losses as well.
At zero slip the tyre produces no net thrust, so the drawbar power is zero and TE is zero. As slip rises, net traction rises quickly at first, because more soil is mobilised in shear, then levels off as the soil's shear strength is used up. The speed loss, meanwhile, grows in direct proportion to slip. The product (NT/GT)(1 − s) therefore rises to a maximum and then falls. The slip at which TE peaks depends on the soil: on firm soil it occurs at lower slip and on loose, tilled or sandy soil at higher slip. Many texts quote an efficient working band of roughly 10 to 15 percent for tractors on agricultural soils, rising towards the upper end on loose soil, and ASABE machinery management guidance gives slip ranges that increase from hard surfaces to soft soils. A rule of thumb follows: if slip is well below the band, the tractor carries too much ballast for the job (wasting fuel moving weight and compacting soil); if well above it, the tractor needs more ballast or less load.
The power chain of a tractor is: engine flywheel power, less transmission losses, gives axle power; axle power times tractive efficiency gives drawbar power. Maximum tractive efficiencies of tyres are high on concrete and fall progressively on firm, tilled and soft soils. Tracks and well-ballasted four-wheel-drive tractors usually achieve higher tractive efficiency than two-wheel-drive tractors on soft or tilled soil, because they spread the load over a larger contact area and share thrust between more driving elements. Tractor test codes, such as the OECD standard code for the official testing of agricultural and forestry tractor performance (Code 2) and national test codes, report drawbar performance on a specified test track, usually concrete or firm ground. Field drawbar power on tilled soil is lower, so an engineer uses test-track data to compare tractors, not to predict field output directly. A worked chain makes the point: an engine delivering 40 kW through a transmission of 90 percent efficiency puts 36 kW on the axles; at a tractive efficiency of 70 percent only about 25 kW reaches the drawbar.
Agricultural drive tyres carry load on air: at a given inflation pressure, a tyre deflects until its contact area times an effective pressure (inflation pressure plus a contribution from carcass stiffness) supports the load. Lower inflation pressure lengthens the contact patch, increases contact area, lowers ground pressure, reduces rolling resistance on soft soil and improves traction, but each tyre has a minimum pressure for a given load and speed set by the tyre manufacturer's load tables; running below it damages the carcass. Bias-ply tyres have cords crossing at an angle and stiff sidewalls; radial-ply tyres have cords running radially with a separate belt under the tread, flexible sidewalls and a longer, flatter footprint, and usually give higher tractive efficiency and lower compaction at the same load. Size markings follow a pattern: a bias-ply marking such as 13.6-28 gives nominal section width in inches and rim diameter in inches; a radial may show 13.6R28, or a metric form such as 340/85R28 with section width in millimetres, aspect ratio (section height as a percentage of width) and rim diameter in inches. Lugs (bars) on the tread penetrate soil and engage it in shear; their height, angle and spacing trade traction against self-cleaning, ride and road wear.
Several radii describe a tyre. The unloaded radius is half the overall diameter. The static loaded radius is the distance from axle centre to ground under load. The rolling radius (or dynamic rolling radius) is the distance travelled per revolution divided by 2π in a stated condition, and it lies between the two. Speed calculations and slip use the rolling radius, not the unloaded one; using the nameplate diameter overstates theoretical speed and so overstates slip. Tyre deflection δ, the difference between unloaded and loaded section height, appears in the Brixius mobility number because a softer, more deflected tyre acts on the soil over a longer contact. On four-wheel-drive tractors with smaller front than rear tyres (mechanical front-wheel drive), the gear ratio to the front axle is chosen so the front wheels run slightly faster in theoretical speed than the rears. This small positive lead avoids the front tyres braking the tractor; too much lead or wrong tyre sizes cause tyre scrubbing, wear and a circulating power loss called power windup.
A track lays its own long flat contact, so for the same load it gives a much larger contact area and lower mean ground pressure than a wheel. Mean ground pressure is the load divided by total track contact area, W / (2 b l) for two tracks each of width b and ground contact length l. Real pressure under a track is not uniform; it peaks under each road wheel, so peak pressure is several times the mean, especially with few rollers and a slack track. Thrust, from Micklethwaite's relation applied to the whole contact, is H = 2 b l c + W tan φ, so in cohesive soil the long contact gives much more thrust than a wheel. Tracks also develop thrust at lower slip, because shear displacement builds along a long contact length, giving higher tractive efficiency on soft or tilled soil. Their drawbacks are higher cost, more internal friction in the running gear, harder steering (skid steering scuffs soil in turns), limited road speed and wear. Rubber tracks on agricultural tractors narrow the gap in road use. Half-tracks and rubber-tracked undercarriages are used on combines in wet harvest conditions.
The cone penetrometer is the simplest field measure of soil strength for machine work. A cone on a shaft is pushed vertically into the soil at a steady rate and the force is recorded; the cone index (CI) is the force divided by the base area of the cone, reported in kilopascals or megapascals. ASABE Standard S313, Soil Cone Penetrometer, specifies a 30-degree circular stainless-steel cone. The larger cone has a base area of 323 mm² (base diameter 20.27 mm) on a 15.88 mm shaft and is recommended for soft soils; the smaller cone has a base area of 130 mm² (base diameter 12.83 mm) on a 9.53 mm shaft and is recommended for hard soils, where the larger cone would need an impractically high force. ASABE EP542, Procedures for Using and Reporting Data Obtained with the Soil Cone Penetrometer, sets the insertion rate at about 30 mm/s and asks that moisture content be measured alongside, because CI falls strongly as the soil wets. Readings vary a lot from point to point, so many insertions are averaged, and results are usually reported as a profile of CI against depth.
Cone index is a composite: it combines shear strength, compressibility and soil-metal friction on the cone into one number. It is therefore not a fundamental soil property, but it correlates well with vehicle performance because a tyre loads soil in a similarly mixed way. That is why the Wismer-Luth and Brixius traction equations use CI. For tyre prediction the CI is averaged over the depth the tyre influences, commonly the top 150 mm. CI profiles also map compaction: a plough pan or traffic pan shows as a sharp rise in CI at a particular depth, and farmers use this to decide whether and how deep to subsoil. A cone resistance of around 2 MPa is widely cited as the level at which root elongation of many crops slows markedly, though the exact threshold varies with crop, soil and moisture. Handheld penetrometers with a spring or electronic load cell and a depth sensor are standard field tools; tractor-mounted and vehicle-mounted penetrometers allow many readings for mapping. Always report the cone size, moisture content and depth with a CI value.
Tractor chassis mechanics is the static and quasi-static equilibrium of the tractor as a rigid body. For a two-wheel-drive tractor on level ground pulling a trailed implement, the forces are: total weight W acting at the centre of gravity, a horizontal distance x ahead of the rear axle; the vertical soil reactions Rf at the front wheels and Rr at the rear wheels; the rolling resistance of the front wheels, acting at ground level and opposing motion; the net thrust of the rear wheels at ground level; and the drawbar pull P, acting at the hitch point at height h above the ground. Taking moments about the rear wheel contact point, horizontal forces at ground level have no arm. Hence Rf × L = W x − P h, where L is the wheelbase, so Rf = (W x − P h)/L and Rr = W − Rf. Horizontal equilibrium gives rear net thrust equals P plus front rolling resistance. This equilibrium is the foundation for weight transfer, longitudinal stability and ballast decisions.
Looking at the rear wheel alone, the axle torque T turns the wheel, and the soil pushes forward on the tyre. The reaction torque on the tractor body is equal and opposite: the body tends to rotate backwards about the rear axle, lifting the front. In steady motion this reaction is balanced by the front axle load and the weight moment. If the wheels are stalled or the clutch is engaged suddenly with the rear wheels held, the torque reaction can rise faster than the body weight can resist and the tractor rears up, which is the mechanism of rearward overturning. A hitch that is too high or a drawbar pull that lies above the rear axle makes this much worse. For this reason drawbar heights are limited by standard and the drawbar is placed below the rear axle centreline, and tractor operators are taught never to hitch loads to the axle housing or the top link point.
Implements carried on the three-point linkage do not pull at a single hitch point. The two lower links and the top link form a linkage whose lines, when extended, meet at an instantaneous centre of rotation, the virtual hitch point. The implement's soil force, its weight and the link geometry determine how much vertical load is transferred to the tractor's rear axle and how much is taken from the front. A mounted plough adds both its own weight and a portion of the downward soil force to the tractor, which is one reason mounted and semi-mounted implements often need less ballast than trailed ones of the same draft. Draft control senses the force in the linkage, commonly in the top link or the lower links, and raises the implement slightly when draft rises, keeping draft and thus wheel slip within bounds; position control holds the implement at a set height regardless of draft. Mixed control combines both. The line of pull, from the virtual hitch point through the implement's centre of resistance, should be set as the implement's manual prescribes; a steep line of pull transfers more weight to the rear wheels but also tends to lighten the front.
When a tractor pulls, weight moves from the front axle to the rear axle. From the chassis equilibrium, the change in front axle reaction compared with the static value is −P h / L, and the rear axle gains the same amount. So the weight transfer is ΔW = P h / L, where P is the horizontal drawbar pull, h is the height of the line of pull above the ground (for a horizontal pull, the drawbar height) and L is the wheelbase. Weight transfer is useful up to a point: the rear drive wheels of a two-wheel-drive tractor gain dynamic load and hence traction, which is why a 2WD tractor can pull more than its static rear weight alone would suggest. It is dangerous beyond that point, because the front wheels lose load, steering weakens and, in the limit, the front lifts. A longer wheelbase reduces transfer; a higher hitch increases it. If the pull is inclined downward at an angle, its vertical component adds load to the rear axle as well, and its moment about the rear contact depends on where it is applied.
Ballast is added mass (cast-iron weights or water or a water-antifreeze solution in the tyres) that raises the dynamic load on the driving wheels. The required dynamic load on the drive wheels is the net pull divided by the net traction ratio achievable on the soil: W_dynamic = NT / NTR. The engineer works backwards: from the needed pull and a target slip, the achievable NTR follows from traction equations, and from NTR the needed dynamic weight; weight transfer supplies part of it, ballast the rest. Too little ballast gives high slip, wasted fuel and tyre wear; too much gives low slip, extra rolling resistance and compaction. Manufacturers and extension guides give recommended static front/rear weight splits for two-wheel drive, mechanical front-wheel drive and four-wheel drive tractors, and a ratio of mass to power for heavy draft and light high-speed work; these guidelines differ by source and should be checked against the tractor's manual. Front ballast on 2WD and MFWD tractors restores steering load lost to weight transfer, and is essential with heavy rear-mounted implements.
On an uphill slope at angle θ, the weight component W sin θ acts downhill through the centre of gravity at height h_g, and its moment about the rear contact point further reduces the front axle load; together with drawbar pull this can lift the front. On a downhill slope, load moves to the front. In four-wheel-drive and MFWD tractors weight transfer also matters: because the front wheels also drive, weight moved off them reduces their thrust, and the tractor's total traction depends on how evenly the dynamic load is shared. For this reason four-wheel-drive tractors are often ballasted to carry more static weight on the front, so that under draft the dynamic loads become nearly equal. The same ideas extend to power tillers: a two-wheel power tiller's handle and tail wheel or implement carry part of the load, and the operator's hand force takes part of the weight transfer.
A tractor is stable longitudinally as long as the front wheels carry a positive load. Setting Rf = 0 in the chassis equation gives the limiting drawbar pull on level ground: P = W x / h. Any combination of pull, hitch height and slope that brings the front load to zero starts rearward overturning. On a static uphill slope with no pull, the tractor overturns backwards when the line of action of weight passes behind the rear wheel contact, that is when tan θ = x / h_g, where x is the horizontal distance from rear axle to centre of gravity and h_g the height of the centre of gravity above ground (both measured on level ground). Dynamic rearward overturning is far more common than static: engaging the clutch abruptly in high gear with a heavy load, pulling from a high point, or trying to drive out of a ditch with the wheels stuck converts axle torque into body rotation in a very short time. Front ballast, correct drawbar height, smooth clutch engagement and driving straight up (and reversing up) steep slopes are the controls.
A tractor with a rigid front axle on a side slope overturns sideways when the weight line passes outside the downhill wheel contacts. For a centre of gravity midway between the wheels, the static limit is tan θ = (t/2) / h_g, where t is the track width. Most agricultural tractors, however, have a front axle that pivots about a central longitudinal pin, so the front axle offers support only at the pivot until it reaches its stop. The effective support is then the stability triangle formed by the two rear wheel contact points and the front axle pivot. Lateral overturning occurs about the line joining the downhill rear wheel contact and the front pivot, which is closer to the centre of gravity than the wheel track would suggest, so the permissible side slope is smaller. Raising a mounted implement, filling a front loader bucket or adding a high load all raise the centre of gravity and reduce it further. Widening the rear track, lowering loads and adding liquid ballast in the rear tyres improve lateral stability.
In a turn of radius r at speed v, a centrifugal force m v² / r acts outward through the centre of gravity. Taking moments about the outer wheels on level ground, the tractor tips when v² / (g r) exceeds (t/2) / h_g, so the critical speed is v = √(g r t / (2 h_g)). A turn on a slope, a bump under the uphill wheel or braking one wheel while turning at road speed can combine with this to overturn a tractor at speeds that seem safe. Because no operator can guarantee stability in every situation, the engineering answer is protection: a rollover protective structure (ROPS), a frame or cab tested to absorb the energy of an overturn and preserve a clearance zone, used with a seat belt so the operator stays within that zone. Test codes published by the OECD and adopted or paralleled in national standards specify ROPS strength tests. Practitioners should check local law: several countries require ROPS on new tractors and some fund retrofits of older ones.
The centre of gravity (CG) of a tractor is found experimentally because the machine is too complex to calculate. Its longitudinal position is found by weighing: place the front axle on a platform scale with the tractor level to read Wf, then the rear to read Wr (or weigh the whole tractor to get W = Wf + Wr). Taking moments about the rear axle, x = Wf L / W, where x is the distance of the CG ahead of the rear axle and L the wheelbase. The lateral position is found the same way by weighing the left and right wheels: the offset from the left wheel line is W_right × t / W. Most tractors have the CG close to the centreline laterally, but a mounted side implement, a loader or unequal ballast shifts it. Record the fuel level, ballast, tyre pressure and any mounted equipment with the result, because each changes the CG.
The height of the CG is found by tilting the tractor. With the tractor level and the front axle on a scale, record the level front reaction Wf. Lift the front axle through a measured angle θ, keeping the rear wheels on the ground and chocked, and record the new front reaction Wf′. Taking moments about the rear axle, with y the height of the CG above the line joining the axle centres, Wf′ L cos θ = W (x cos θ − y sin θ), so Wf′ = W (x − y tan θ)/L and y = (Wf − Wf′) L / (W tan θ). The CG height above ground is h_g = y + the rear axle height (the rear static loaded radius) when the axle centres are level on level ground; if front and rear axle heights differ, allow for the slope of the axle line. When the CG is above the axle line, the front reading falls as the front is lifted; a larger change in reading means a higher CG. Accuracy improves with a larger tilt angle, but the angle must stay small enough that fuel, oil and loose parts do not shift. The front axle pivot should be locked and the tyres held at their working pressure.
Other methods include the suspension method, in which the tractor or a large component is hung from two different points and the CG lies where the plumb lines through each suspension point cross, practical for small machines such as power tillers; the tilt-table method, in which the tractor is tilted sideways on a platform until it is about to overturn, giving the lateral stability angle directly; and the compound pendulum method, which also yields moments of inertia for dynamic overturning analysis. Test institutes measure the CG as part of full tractor tests, and the result feeds stability calculations, ROPS design and ballast advice. For exams, the weighing and tilting methods are the ones asked; the key is to take moments about the right point and to use the rear axle height to convert from height above axle to height above ground. A good check is physical sense: a CG height below the axle centres, or a longitudinal position outside the wheelbase, means a sign or reading error.
Compaction is the increase in bulk density and the loss of pore space, especially large pores, caused by applied stress. A wheel loads the soil surface with a contact pressure and the stress spreads downward and outward. Boussinesq's solution for a point load Q on an elastic half-space gives vertical stress directly beneath the load σz = 3Q / (2π z²) at depth z. Fröhlich generalised this with a concentration factor ν: σz = ν Q / (2π z²), ν = 3 giving Boussinesq. Söhne applied this to agricultural soils, suggesting that stress concentrates more near the load axis as soil becomes softer and wetter, with concentration factors rising from about 4 in hard dry soil to about 6 in wet soft soil. His well-known conclusion, widely confirmed since, is that topsoil stress is governed mainly by contact pressure (roughly inflation pressure for a flexible tyre), while subsoil stress is governed mainly by total axle load. Lower tyre pressure therefore protects the topsoil, but only lighter axle loads protect the subsoil, where compaction is persistent and hard to remove.
Soil is most vulnerable when wet, because water lubricates particle contacts and the soil's pre-compression stress falls. The first pass of a wheel causes most of the compaction; later passes in the same track add less each time but continue to push compaction deeper. Wheel slip adds shear, which smears and compacts the surface of the rut. On many farms a large share of the field area is trafficked each season, much of it by heavy grain carts and slurry tankers during harvest and in wet conditions. The effects are reduced infiltration and drainage, poorer aeration, restricted root growth and yield loss, and extra draft for the next tillage pass. Compaction is detected with cone penetrometer profiles, bulk density cores, visual soil assessment and infiltration tests. Comparing trafficked and untrafficked strips of the same field, at the same moisture, separates traffic compaction from natural dense layers. Readings should be taken at a moisture close to field capacity, because a dry soil gives high cone index even where it is not compacted.
Management starts with avoiding it. Measures include staying off wet soil, reducing axle loads, using low-pressure radial tyres, central tyre inflation systems that lower pressure in the field and raise it on the road, tracks, dual wheels (which reduce contact pressure but spread the stressed zone wider), and matching ballast to the job rather than leaving tractors over-ballasted. Controlled traffic farming confines all wheels to permanent traffic lanes, often using satellite guidance, so that most of the field is never driven on; the lanes become firm, which improves traction, while the crop zone stays loose. Once compaction exists, subsoiling or deep ripping can break a pan, provided the tine works above its critical depth in soil dry enough to shatter; loosened soil is fragile and recompacts quickly if trafficked, so subsoiling should be followed by traffic control. Biological measures such as deep-rooted crops help rebuild pore structure over longer periods.
Lowland rice fields are puddled: the soil is saturated and churned into a soft mud layer over a firmer layer, the hardpan or plough sole, formed by repeated puddling and traffic. Puddled soil has very low shear strength and bearing capacity, almost no friction contribution because pore water carries the load, and a high adhesion that makes mud stick to wheels. The cone index of the mud layer is very low compared with dry-land soils. Traction therefore depends on reaching and gripping the hardpan, or on engaging a large volume of the soft mud. Ordinary pneumatic tyres sink, fill their treads with mud, slip excessively and produce large motion resistance from the bulldozing of mud in front of the wheel. Sinkage also increases with depth of the soft layer, so fields that have been puddled deeply for many seasons are harder to work than lightly puddled ones. The hardpan itself is agronomically useful because it reduces percolation losses of ponded water, so the engineer's goal is to use it without destroying it.
Cage wheels are open steel wheels with transverse lugs or angle-iron bars on a light frame. They sink through the mud to the firmer layer, engage it with their lugs and carry little mud because they are open. They are used on power tillers and as attachments outside or in place of tractor rear tyres. Lug design matters: taller lugs reach firmer soil, lug spacing controls how many lugs are engaged at once, and lug angle affects both thrust and the lifting or throwing of mud; designs have been studied experimentally at rice research institutes in Asia. Semi-cage wheels and high-lug rubber tyres are compromises for tractors that must also run on roads. Floats or sleds under a power tiller or rice transplanter carry part of the weight on the mud surface, reducing sinkage, while the driving wheels provide thrust. Riding-type rice transplanters and harvesters use narrow wheels or rubber tracks designed for this environment.
Traction performance in wetland is poorer than on dry land by any measure: net traction ratios are lower, slip at a useful pull is higher and tractive efficiency is lower. The main losses are the energy spent pushing and lifting mud and the sinkage of the wheel. The rolling resistance of a sinking wheel in soft soil comes largely from the work done compressing and displacing soil to form the rut, which is why Bekker-type pressure-sinkage analysis is used in wetland research. Practical advice for operators includes working the field with the correct water depth, using cage wheels or high-lug tyres rather than standard tyres, avoiding sharp turns that break the hardpan, keeping ballast light enough to avoid excessive sinkage and not over-deepening the puddled layer. Engineers designing wetland machines test them in soil bins filled with puddled soil prepared to a controlled consistency, because field conditions vary too much for clean comparisons.
Learn the handful of equations cold and the reason behind each: slip from speeds or revolutions, GT = torque/radius, NT = GT − RR, TE = (NT/GT)(1 − s), weight transfer P·h/L, front reaction (W·x − P·h)/L, CG by weighing and tilting, and the overturning angles. Draw a free-body diagram for every chassis problem and take moments about the rear wheel contact point. Most lost marks come from using unloaded radius instead of rolling radius, inverting the slip ratio, or leaving centimetres in a kilonewton calculation. In the lab, run a cone penetrometer profile and a drawbar test at least once so the numbers mean something.
A service or extension engineer uses this subject to answer farmers' questions: why the tractor slips, whether to add ballast, what tyre pressure to run, and which implement width a tractor can pull. Measure slip in the field by counting wheel revolutions over a marked distance with and without load. If slip is well below the efficient band, remove ballast; if well above, add it or reduce width or depth. Set tyre pressure from the manufacturer's load table for the actual axle load. Use a cone penetrometer to find plough pans before recommending subsoiling, and set the subsoiler depth just below the pan, above critical depth. Always check ROPS and seat belt condition.
A senior engineer sets policy and designs fleets. The questions are tractor-implement matching across a custom hiring fleet, standard ballast and tyre specifications for each soil zone, controlled traffic layouts, and whether to move to tracks or central tyre inflation. Test data from national testing institutes and OECD reports support procurement decisions, but field tractive efficiency is lower than test-track figures. At this level, safety is systemic: specifying ROPS on every tractor bought, training operators on dynamic rearward overturns, and reporting incidents. Soil compaction is a long-term asset question: heavy axle loads at harvest cause subsoil damage that no tillage fully repairs.
Research in this field is moving from empirical traction equations towards models that couple soil mechanics and machine dynamics: finite element and discrete element simulation of soil-tool and soil-tyre interaction, critical-state soil models for compaction, and in-field sensing of draft, slip and soil strength for automatic ballast and tyre-pressure control. Open problems include predicting traction on tilled and wetland soils where the mobility-number equations were not fitted, predicting subsoil compaction under repeated heavy passes, and scaling from soil-bin tests to fields. A senior researcher also judges the validity range of every empirical coefficient and insists on reporting soil condition with every result.
This manual does not reproduce the coefficient tables of ASABE D497 (they are copyrighted and must be read from the standard), nor tyre load-inflation tables, which are manufacturer-specific. It gives no single value of specific soil resistance, optimum slip or recommended weight split, because these vary with soil, tyre and source. It does not cover finite element or discrete element modelling in depth, dynamic overturning simulation, ROPS test procedures in detail, power hop, or animal-drawn implement traction. Wetland traction is treated qualitatively; published lug-design data vary by study and are not summarised. Country ROPS laws are mentioned only in general terms.
Original practice questions written to the syllabus and pattern of the exams named in each question's examTags. They are not past papers and do not reproduce any board's questions.
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