Both the tire and the shock absorber absorb the energy to cushion the impact of an aircraft’s vertical descent rate at landing in order to maintain structural integrity and avoid the tire bottoming out. FAA safety requirements limit the vertical descent velocity, VVert> for civil aircraft applications; military specifications limit military applications. Table 7.1 lists limits for various types of aircraft. In turn, VVert produces g-load at the sudden termination of VVert at landing – it can be expressed as load factor n (see Section 5.5). Equation 5.4 gives n = (1 + a/g); it is loosely termed as the number of the g-load; for an undercarriage design, it is designated ni (see Table 7.1). During landing, nl takes a positive value; that is, it would experience heavier weight. For example,
nl = x (a number) means that the weight has changed by x times. (7.10)
These are extreme values for safety; in practice, 4 fps is a hard landing in a civil aircraft operation. The maximum landing aircraft mass ML is taken as 0.95 MTOM for aircraft with a high wing-loading.
The vertical velocity kinetic energy to be absorbed is
Eab = 1/2Ml X VVert2 (7.11)
This is the energy to be absorbed by all the main wheels (m wheels) and struts (n struts) at touchdown during landing. The nose wheel touches the ground much later, after the main wheels have already absorbed the impact of landing.
Eab = Eabstrut + EabJire (7.12)
energy absorption by strut (Let n be the number of struts.)
Assume that a landing is even and all struts have equal deflection of 5strut.
Then, energy absorbed by all the struts is
Eabstrut = n X nl X gML X kstrut X ^strut, (7.13)
where kstrut is an efficiency factor representing the stiffness of the spring and
has values between 0.5 and 0.8, depending on the type of shock absorber used.
In this book, 0.7 is used for modern aircraft and 0.5 is used for small club and homebuilt categories.
energy absorption by tire (Let m be the number of tires.)
Assume that a landing is even and all tires have equal deflection of 5tire. Then, energy absorbed by all the tires is
Eab-tire = m X Hi X gML X ktire X Stire (7.14)
where ktire = 0.47 is an efficiency factor representing the stiffness of all types of tires.
The following can be written by equating Equation 7.11 with Equation 7.12 and then substituting Equations 7.13 and 7.14 in Equation 7.12 and replacing ni by Equation 7.10. Here, the load factor ni is replaced by x:
Eab =    /2Ml X VVet = H X x X gML X kstrut X 5strut + m X x X gML X ktire X Stire
Simplifying as follows:
(1/2 X VVert)/g = xx(h X kstrut X Sstrut + m X ktire X Stire) (7.15)
7.9.1 Deflection under Load
The total vertical deflection of the strut and tire during landing can be computed by using Equation 7.15. Other types of lateral strut deflection during turning and other maneuvers are not addressed in this book.
Total deflection is
S = strut + Stire (7.16)
It is recommended that a cushion be kept in the strut deflection (compression) so that ends do not hit each other. In general, 1 inch (2.54 cm) is the margin.