• Section 13.2 presents important information about wheels, tires, and brakes used for aircraft, allowing the reader to size and select these landing gear components. Additionally, a number of important concepts regarding fixed and retractable landing gear are presented. It is recommended that the reader is familiar with these before beginning the layout of the landing gear.

• Section 13.3 presents cookbook methods to place the nose, main, and tail wheels of the airplane, for conventional, taildragger, and monowheel configurations. Additionally, methods of calculating the reaction loads for the landing gear and to evaluate the airspeed required to rotate the airplane during T-O are presented.

Positioning

The main and auxiliary landing gears (nosewheel, tail wheel, etc.) must be properly positioned with respect to the CG to reduce the risk of ground looping, overturning, crosswind canting, tail angle, and to allow the airplane to be maneuvered as needed during the T-O and landing ground run. Methods that address this are presented in the following sections:

The designer should keep in mind that an efficient structure places stout structural elements near the hardpoints for the landing gear so extra support structure will not be called for.

Ground Clearance

A well-designed landing gear provides adequate clearance between the ground and all other parts of the airplane, even in the worst combination of flat tire and deflated oleo-pneumatic shock absorber. This means propeller tips, nacelles, wingtips, deflected flaps, and so on. A tailskid or bumper should be installed to prevent damage to the airplane from a tail strike.

Landing Gear Component Vendors

Table 13-2 lists a few companies that manufacture and sell components for landing gear.

Tires and Tire Inflation Pressure

The inflation pressure should be selected based on the weight of the aircraft, number of tires, and the bearing capability of the airfield from which the airplane will be operated.

Nosewheel tire pressure should be based on allowable dynamic loads as follows:

Main gear tire should allow for 25% growth in aircraft gross weight. The main gear tire load rating should be based on maximum gross weight and adverse CG location. Forged aluminum-alloy wheels are recommended.

Landing Impact and Braking

The landing gear is required by applicable regulations to react a number of landing scenarios. For GA aircraft, the applicable landing gear loads are stipulated by 14 CFR 23.471 to 23.511. For seaplanes, the hull landing loads are stipulated in 14 CFR 23.521 to 23.562. For land planes, there are individual requirements for landing on the main gear only, three-point landing, and side impact loads. The magnitude of these loads is very high and they are reacted as point loads in the airframe. In addition to the impact forces, the landing gear should provide good damping characteristics and should permit the aircraft to taxi over uneven ground without transmitting excessive shocks to the airframe. The airplane should possess a good, reliable, and safe braking system so that it can handle all braking conditions. It should offer a parking brake that can hold the airplane at gross weight on a 1:10 gradient slope or on a level runway with maximum T-O power applied on one engine. Anti-skid brakes are recommended.

Turning Radius

For maneuvering on the ground, in particular when turning into position on a narrow runway, the turning radius is a very important feature in aircraft ground operation. Figure 13-3 shows how the turning radius for a given rotation of the nose landing gear can be determined. The distance h denotes the location of the center of turn and can be calculated using:

Equation (13-2) below allows the turning radius to be calculated, knowing only the wheelbase and the turning angle of the nose gear.

Some aircraft are capable of turning on a dime, literally, by enabling a large enough nose gear turning angle. This requires the nose gear to be capable of turning at least:

(13-3)

Tire Footprint

A tire in contact with the ground will flatten slightly on the bottom so its contact area resembles that of an ellipse (see Figure 13-4). The weight, F, supported by the tire is distributed over this area, generating an average pressure, P, on the area which amounts to:

(13-4)

The higher the pressure inside the tire, the less are the values of a and b. High-pressure tires supporting large loads may cause rutting damage to the runway. On soft enough ground, the tire may sink, which explains why high-floatation tires (so-called “Tundra tires”) have both a large diameter and low internal pressure. Note that the dimension a is usually taken to be 85% of the distance c.

Note that the compression of the tire increases the internal pressure due to the reduction of internal volume. The unloaded pressure is therefore always lower than the loaded one. Inflation pressure reported by manufacturers refers to the unloaded tire at standard S-L temperature. Typically, when the tire is loaded to the rated load, the pressure will be approximately 4% higher than the rated pressure. Tires should always be allowed to cool for at least an hour before checking the pressure.

Equation (13-4) can be used to estimate the required internal pressure for a tire if the allowable ground pressure limits are known for a particular runway or taxiways. Effectively, P equals the internal tire pressure.

Manufacturers’ data, such as that of Ref. 2, tabulates the loaded radius, R_L, enabling the estimation of the dimension a in Figure 13-4. The first step is relating it to the distance c as shown below:

The value of a is usually about 85% of c. Therefore, the dimension can be calculated as follows:

(13-5)

Castering Nose and Tail Wheels

The use of castering nose landing gear and tail wheels in taildragger aircraft is a common solution for steerable landing gear in many light GA aircraft. The steering is usually implemented using differential braking, i.e. the pilot steps on the left or right rudder pedals to generate braking in the corresponding main wheel, which turns the aircraft on the ground.

The most common problem with castering landing gear is shimmy, which is a violent oscillation that is a function of speed and the inertia characteristics of the landing gear. Shimmy can begin when the aircraft moves over uneven ground, and even due to worn tires or landing gear parts. It ranges from a simple wobble to an oscillation so violent it literally breaks the landing gear off the airplane. For this reason, castering landing gear is sometimes equipped with a small device called a shimmy damper, which most often is a small cylinder filled with hydraulic fluid that has a piston inside that connects to the movable (rotational) part of the landing gear.

Several configurations are shown in Figure 13-5. Their properties are shown in Table 13-3.

Tire Types

Of the number of standard tire designations used for aircraft, the ones presented in this book are based on definition by the Tire and Rim Association (TRA), which is the technical standardizing body of tires and rims in the USA. TRA designations for common tires are shown in Table 13-4. Note that the Three Part Type designation is the modern system. The designer of certified GA aircraft will pick the Three Part Type designation, whereas the designer of homebuilt aircraft can resort to other types of tires.

Inflation Pressure

The tire maintains its shape as a consequence of the inflation pressure. Tires are very flexible in bending but have very limited extension (or stretch). As the tire reacts loads its cross-section flexes and a side force will be generated on the flange of the rim. The tire is designed to operate at an approximately 32–35% deflection under static load, but this means it will bottom out at around 3× the static load. Shock absorbers are designed to bottom out at 3× the static load as well, and are intended to do so before the tire¹. Table 13-5 shows ranges of pressure for various applications.

Tire Geometry

The following parameters are important when discussing tires (refer to Figure 13-7):

Ensure there is no confusion with the AR of a wing. A low tire AR means it is wider than it is high. Such tires are intended for high speeds on smooth surfaces. High-AR tires are meant for rough field operations that call for improved floatation.

An LR of 1.5 to 2.0 is considered low, while 2.0 to 2.5 is desirable [1].

Tire Sizes

Unfortunately, when it comes to specifying tire sizes there is no one standard, but rather several that have evolved since the inception of tire standardization in 1903. This results in several choices at the disposal of the designer, although focusing on the Three Part Type is recommended for modern aircraft design. The TRA type tires shown in Table 13-4 have the sizing designation shown in Table 13-6. Figure 13-8 shows schematics of the three most common types, Type III, VII, and the Three Part Type.

Selection of Tire Sizes

The first step is to download a document like Ref. [2], which features an excellent selection guide in Section 4 – Data Section – Tires. The document lists tires by type and rated speed, load, inflation pressure, braking load, and bottoming load. It is an ideal resource to pick a potential tire during the conceptual and preliminary design phase. It can be downloaded free of charge from: www.goodyearaviation.com/resources/. Also, note that for the certification of GA aircraft, the tire selection is bound by 14 CFR 23.733 Tires.

It is problematic that Type III do not explicitly specify the nominal diameter of the tire. For specific dimensions refer to Ref. 2.

Main wheel tires: select main landing gear tires in accordance with the following guidelines:

Nosewheel tires: select nose landing gear tires in accordance with the following guidelines:

Tail wheel and outrigger wheels: for smaller aircraft, the tail wheel and outrigger wheels are solid rubber. For larger aircraft, inflated tires are used and can be selected using a similar approach to the above. In the absence of rational analysis, if the outrigger wheels are intended to support landing impact, the attachment structure should be capable of supporting a vertical and side load amounting to 1/2 g. The wheel can then be selected based on the resulting load. For example, an airplane with an outrigger and 1000 lb_f gross weight would be reinforced to react 500 lb_f acting at the tire. This side load requirement is in accordance with 14 CFR 23.485 Side Load Conditions, although the regulations do not specifically address outrigger configuration. There is no set rule in outrigger structure. Aircraft like the Fournier RF-1 and RF-3 use outriggers not capable of reacting the above load, albeit sufficient to support taxi loads. The Fournier RF-2 does not even use wheels, but rather a wire loop, each end of which is mounted to the wing structure.

Wheels

The modern wheel is usually made from forged aluminum or magnesium alloy. Aluminum wheels are heavier, but are less expensive and have better corrosion resistance. Both are equal in robustness and have the same performance rating.

Wheels usually consist of two halves that are joined together by bolts (see Figure 13-9). Some modern designs are of a single-piece configuration that is easier to manufacture and maintain. They feature special lock-rings to provide the necessary lip for the tire.² The wheel contains tapered roller bearings that are a press fit into a space called the bearing housing. They are kept in place by spring-fit snap rings. Brake discs are often attached to the wheels using the fasteners that hold the two halves together.

There are three common sizes of wheels for small aircraft: 5′′, 6′′, and 7′′ diameter. The diameter (Dia) is measured between the wheel shelves as shown in Figure 13-9.

Brakes

The brakes must provide the airplane with a means to: stop the aircraft after landing or an aborted take-off; keep the airplane at rest at full power (this means the critical engine only for a multi-engine aircraft); allow the airplane to be steered via differential braking or appropriate slow-downs during taxiing; and park. The brakes are not expected to retain the aircraft with the wheels locked should there be enough thrust to move the aircraft. A simplified schematic of the brake system in a light aircraft is shown in Figure 13-10.

There are two common kinds of brakes: drum brakes and disc brakes. Drum brakes usually reside inside the wheel, which reduces their frontal area and, if mounted on retractable landing gear, makes them a possible solution for space-claim issues in thin wings. Disc brakes have superior performance, are lighter, and easier to maintain.

The application of brakes generates considerable heat through friction. The amount of heat depends on factors such as the weight of the vehicle being stopped, the speed at which braking is applied, the effectiveness of the conversion of friction into heat, and the friction area of the brakes. This is where the difference between drums and discs become apparent. Drum brakes dissipate heat far less effectively than disc brakes. Since the brake is contained inside the wheel the result is inferior heat transfer from the drum and if too much heat is generated the braking capacity is lost (“fading”) just when it is needed the most. In contrast, disc brakes reside on the outside of the wheel and are directly exposed to air, in addition to featuring calipers with two braking pads on each side of the disc (and sometimes multiple discs). Direct exposure to air leads to superior cooling and more effective braking under demanding conditions.

Manufacturers recommend that wheels and brakes be selected together. These should be selected in accordance with the following guidelines:

where

Equation (13-6) yields the kinetic energy per brake and this value must be specified when contacting brake manufacturers.

Derivation of Equation (13-6)

For V_S0 in ft/s or m/s and m in slugs or kg, the kinetic energy is given by:

The above regulatory paragraph assumed V_S0 in KTAS and W in lb_f. Therefore,

QED

Other Useful Information

Aircraft tires are designed such that the internal tensile forces in each fabric layer are uniform when unloaded. When deflected, this force will vary from higher in the outer plies to lower in the inner ones. This variation generates shear stresses in the tire that must not be exceeded. Exceeding this is possible if the tire is under-inflated or over-loaded. This will cause a large deflection that leads to heat build-up which can cause ply separation and rapidly decrease the durability of the tire. It will also cause an uneven wearing of the tread and deterioration of the shoulder, in addition to possible damage to the sidewall of the tire during high impacts (landing). Excessive inflation pressure can also be detrimental due to uneven tread wear and reduced braking effectiveness, as well as making the tire more susceptible to damage by foreign objects.

Tires can withstand reasonably high temperatures, with typical maximum operational limits being a surface temperature that exceeds 225 °F (107 °C) or brake heat reaching a temperature of 300 °F (149 °C). Such a temperature can result from excessive braking after a high-speed landing.

Finally, when selecting wheels and tires, it can be helpful to know the types of tires used for existing fleets of aircraft. Tables 13-7, 13-8, and 13-9 provide such information for selected aircraft of various classes. The reader is directed toward Ref. 2 for more details.

Leaf-spring Landing Gear (A)

The leaf-spring landing gear, as the name implies, consists of a relatively flat but stiff cantilever beam that reacts landing loads in bending. The primary advantage of such landing gear is that it is inexpensive, stout, durable, and is relatively easy to mount to an airplane. It really represents the simplest form of the landing gear. The leaf-spring landing gear is generally used as the main landing gear. Its relatively low thickness-to-chord ratio renders it a relatively low-drag external structure, although the wheels, tires, and braking calipers generate substantial drag and should be covered using a wheel fairing. The primary drawbacks are high reaction loads in the airframe, as the spring beam tends to have a large moment arm. Also, the landing gear does not lend itself well to a retractable configuration. Some Cessna aircraft feature retractable cantilevered landing gear that resembles leaf-spring gear, but really consists of tubular geometry. The leaf-spring has limited structural damping, but works well because of the damping provided by the scrubbing motion of the tires. It has a poor efficiency as a shock absorber, something remedied by the scrubbing motion as well. To the best knowledge of the author, the largest aircraft to currently use a leaf-spring landing gear is the de Havilland of Canada DHC-6 Twin Otter, with a maximum gross weight of 12,500 lb_f.

Oleo-pneumatic Landing Gear (B, C, D)

(B), (C) and (D) in Figure 13-13 are types of landing gear that use a mechanical oleo-pneumatic shock absorber of the type shown in Figure 13-14. Such a shock absorber initially presses the oil against air or nitrogen, while dissipating the impact energy by forcing the oil to flow through a number of recoil orifices. This allows the shock from the landing impact to be reacted initially with a short deflection, and then a larger one as the oil seeps back into its chamber. Reference 4 provides methods to size oleo-pneumatic struts.

Oleo-pneumatic Trailing-link Landing Gear (C)

The oleo-pneumatic trailing-link landing gear has become a popular option in many aircraft due to the superior ride quality it offers on uneven ground. This is possible as the mechanism allows for much larger deflection of the wheel and tire assembly than is possible when mounted directly to the strut. The drawback of the trailing-link landing gear is its greater weight and cost. It also requires a larger internal volume to stow.

Various Landing Gear Issues – Shimmy

Shimmy is a violent dynamic instability that occurs, primarily in free-castering landing gear, due to unbalancing of the forces that act on the members of the trailing link. This is a frequent issue that can be violent enough to break off the nose landing gear. It is therefore of substantial importance to the manufacturer and operator alike. The aircraft designer should be aware of it and possible solutions (shimmy dampers, high-friction castering, geometric relations, mass balancing, and so on).

Various Landing Gear Issues – Whistling

Whistling is a phenomenon in which the complex geometry of a landing gear exposed to the airflow in flight generates a high-pitched audible sound. One aircraft that repeatedly generates this sound is the Piper PA-28 Arrow with its retractable landing gear extended. There is not much that can be done to eliminate the whistling. The author is not aware of any particular studies that have been performed to evaluate the source either of the sound or of potential solutions.

Various Landing Gear Issues – Non-linear Loads During Retraction and Deployment

During the retraction or deployment of landing gear, the actuation system (linkages and hydraulic actuator) undergo variable loading. An actuator capable of brisk retraction or extension during ground tests (when airspeed in zero) may turn out to be grossly undersized when air loads compound the inertia loads. For instance, consider the retraction of a main landing gear into a wing, exemplified in Figure 13-15. As the gear rotates into the wheel well, the air loads acting on the landing gear door (whose effect is attenuated by the complex flow field around the landing gear leg and wheel) may overload the actuator unexpectedly (well, only prior to you reading this) so the gear is stuck in a partially retracted position. It might get stuck at a ϕ ranging from 30° to 60°. This may cause a serious problem in a flight test if the actuator is undersized – it should always be oversized so it has adequate power to power the gear. The test pilot should be ready with a contingency plan – for instance, try retraction just above stalling speed.

(1) A side view of the design in a cruise attitude. Draw the mean geometric chord (MGC) on the side view.

(2) A top or bottom view of the airplane.

(3) A completed CG envelope.

Step 1

Draw the forward CG limit.

Step 2

Draw the aft CG limit.

Refer to Figure 13-20 for Steps 3 through 7.

Step 3

Determine the highest vertical CG location at the aft CG limit and plot on the diagram as shown. This position is the most critical as it is the first point to cross the vertical line drawn in Step 7. If that happens, the plane will fall on its tail.

Step 4

Draw the prop-strike limit as shown, ensuring it is parallel to the ground plane. This is as close to the ground the propeller should get under most adverse conditions, such as with a flat nose gear tire. The limit per 14 CFR 23.925(a) is 7 inches.

Step 5

Draw the tail-strike line as shown, ensuring it is at an angle of α_stall in the clean configuration (because this is the highest angle) up to a maximum value (recommended) of 15°. The tail strike line is also the ground line.

Step 6

Draw a line through the CG perpendicular to the tail-strike line. This is where the contact point of the tire should be, at static deflection of 1 g load. IMPORTANT: This is the static deflection of 1 g load. The landing gear will drop below the tail strike line once it is off the ground.

Step 7

Draw a vertical line through the intersection of the tail-strike line and the normal to it. It should form the same angle as the tail-strike line does to the horizontal. If done correctly, the three lines should all intersect at the same point.

Refer to Figure 13-21 for Steps 8 and 9.

Step 8

Position the main landing gear such the contact point of the wheel is at the intersection of the three lines as shown in Figure 13-21. If practical, align the main landing gear leg along the vertical line.

Step 9

Position the nose landing gear so it carries no more than 20% of the aircraft weight when the CG is at the forward limit, and no less than 10% when the CG is at the aft limit. Too much nose gear load will simply make it harder to rotate the airplane for lift-off. Too light a load will make steering the aircraft harder because of reduced ground friction. A light nose gear load can also promote “porpoising” on the ground.

A few more steps are required to properly position the landing gear.

Overturn Angle

The following steps are intended to verify that the wheel track is wide enough to provide lateral stability when taxiing and turning a corner. Since the CG is located distance h_CG above the ground, the centrifugal force it generates as the airplane turns will result in an overturning moment that can roll the airplane on the wing to the outside of the trajectory. To minimize the risk of this, the designer should check that the combination of wheel track and h_CG will not cause this to take place. As a rule of thumb, the closer to the ground the CG is, the better will be the lateral stability of the airplane. The farther forward the CG, the less is the lateral stability.

Refer to Figure 13-22 for Steps 10 through 14.

Step 10

Draw a line through the center of the contact points of the nose and the left or right main landing gear as shown in Figure 13-22. Here, the right landing gear has been chosen (note that we are looking up on the bottom of the airplane, so the right wing appears to the left).

Step 11

Draw a line through the CG that is parallel to the line drawn in Step 10. For clarity, draw both lines far enough from the airplane to allow additional lines to be marked with ease.

Step 12

Draw a line that is perpendicular to the lines drawn in Step 10 and Step 11. This line represents the ground.

Step 13

Place the CG distance h_CG above the ground line, along the line drawn in Step 11, as shown in Figure 13-22. Also refer to the definition of the h_CG in Figure 13-21.

Step 14

Draw a line that extends from the intersection of the line drawn in Step 10 and the ground line drawn in Step 12, to the CG. This line represents the overturn angle, θ. This angle should be less than 63° for general land-based aircraft and 54° for carrier-based aircraft. If it is larger, then any of the following measures can be taken (provided preceding requirements are not violated):

(1) A side view of the design in a cruise (or tail-off-ground T-O) attitude. Draw the mean geometric chord (MGC) on the side view.

(2) A top or bottom view of the airplane.

(3) A completed CG envelope.

Step 3

Determine the highest vertical CG location at the forward and aft CG limits and plot on the diagram as shown. These two positions are critical to the proper positioning of the main landing gear.

Step 4

Draw the prop-strike limit as shown, ensuring it is parallel to the ground plane. This is as close to the ground as the propeller should get under most adverse conditions, such as with a flat nose gear tire. The limit per 14 CFR 23.925(a) is 9 inches.

Step 5

Draw a line at an incline of 15° that goes through the forward CG location. Note that some references cite 16°, but either one will work just fine.

Step 6

Draw a line at an incline of 25° that goes through the aft CG location. For most aircraft the CG envelope is enclosed between these two lines.

Step 7

Locate the intersection of the lines in Step 5 and Step 6. This is where the contact point of the tire should be, at a static deflection of 1 g load. Draw a line at an incline of 12° to 15° that goes through this intersection, as shown in Figure 13-23. This line represents the ground and should be used to place the tail wheel. Note that the incline of the line shown is 12°. Note that, ideally, the angle of incidence made by the MGC with respect to the ground line should be that of α_stall up to a maximum value (recommended) of 15°.

Refer to Figure 13-24 for Steps 8 and 9.

Step 8

Position the main landing gear so the contact point of the wheel is at the intersection of the three lines as shown in Figure 13-24.

Step 9

Position the tail wheel landing gear such it carries no more than 5% of the aircraft weight when the CG is at the forward limit, and no greater than 10% when the CG is at the aft limit. Too much load on the tail wheel will make it harder to raise the airplane during the ground run. Too light a load will make steering and controlling the aircraft in a crosswind harder because of reduced ground friction.

Step 10

It is imperative that the main landing gear wheel track is wide enough to guarantee the airplane is stable while it corners on the ground. Ensure the width between the tires, W_t, is large enough so the overturn angle is 25° or greater (see Figure 13-25).

Nose gear reaction, R_N:

(13-7)

Main gear reaction, R_M:

(13-8)

where

L_W = wing lift, in lb_f or N

L_HT = horizontal tail lift, in lb_f or N

M_W = pitching moment, in ft∙lb_f or N∙m

T = thrust, in lb_f or N

Special Case – Static Loads

For this case V = 0 and T = 0 (note that this makes friction irrelevant as it only affects the aircraft in motion), leading to the following results:

(13-9)

Note that since the location of the CG is used as a reference in this formulation, a question of sign convention might be raised. For instance, in Figure 13-28, should x_M have a positive sign and x_N a negative sign? What about the forces?

The formulation setup here assumes absolute values of all dimensions and forces. Signs are taken care of in the formulation of both forces and moments. The only exception is the sign of M_W, which is typically negative (nose pitch-down). Its sign is the only one that must be accounted for when using the formulation.

Definition of Aerodynamic Loads

The following formulation of the lift and thrust is convenient, as it allows the designer to evaluate the impact of various aerodynamic characteristics on the landing gear reaction forces. For instance, if a spreadsheet has been prepared, the designer can evaluate the airspeed when rotation to lift-off can be achieved, and evaluate design changes to modify it if necessary.

Derivation of Equation (13-7)

QED

Tail wheel reaction, R_T:

(13-10)

Main gear reaction, R_M:

(13-11)

where

L_W = wing lift, in lb_f or N.

L_HT = horizontal tail lift, in lb_f or N

M_W = pitching moment, in ft∙lb_f or N∙m

T = thrust, in lb_f or N

Special Case – Static Loads

As already discussed in Section 13.3.4, Tricycle landing gear reaction loads, the formulation is set up assuming absolute values of all dimensions and forces. With the exception of M_W, the proper signs are taken care of in the formulation of both forces and moments.

Another confusion that might arise is the direction of LHT, shown as pointing downward in Figure 13-31. Strictly speaking the direction of this force, as setup for the derivation below, does not matter. What matters is that the force direction is already defined as positive upward. If the elevator is neutral (as is shown in the figure) the force would actually point upward (in the positive direction). This would cause a tendency to lift the tail off the ground.

Derivation of Equation (13-10)

QED