The damped unbalance response analysis in accordance with Annex I from API 11th was performed, and total four 4 times of the allowable unbalance weight was applied on this analysis. See below figure for amount of unbalance applications.
The unbalance response was calculated for new and worn clearances respectively, and below figures show responses computed throughout the entire speed range of the pump for the unbalance case 1. The operating deflected shape with criteria at rpm is shown in below figure. The motion of a body through a flow is considered, in flight dynamics, as continuum current. In the outer layer of the space that surrounds the body viscosity will be negligible.
However viscosity effects will have to be considered when analysing the flow in the nearness of the boundary layer. Under these conditions, drag and lift coefficient are functions depending exclusively on the angle of attack of the body and Mach and Reynolds numbers.
Aerodynamic efficiency, defined as the relation between lift and drag coefficients, will depend on those parameters as well. It is also possible to get the dependency of the drag coefficient respect to the lift coefficient. This relation is known as the drag coefficient equation:.
The aerodynamic efficiency has a maximum value, E max , respect to C L where the tangent line from the coordinate origin touches the drag coefficient equation plot. The drag coefficient, C D , can be decomposed in two ways. First typical decomposition separates pressure and friction effects:.
There's a second typical decomposition taking into account the definition of the drag coefficient equation. This decomposition separates the effect of the lift coefficient in the equation, obtaining two terms C D0 and C Di. C D0 is known as the parasitic drag coefficient and it is the base drag coefficient at zero lift.
C Di is known as the induced drag coefficient and it is produced by the body lift. If the configuration of the plane is symmetrical respect to the XY plane, minimum drag coefficient equals to the parasitic drag of the plane. In case the configuration is asymmetrical respect to the XY plane, however, minimum drag differs from the parasitic drag. On these cases, a new approximate parabolic drag equation can be traced leaving the minimum drag value at zero lift value.
The Coefficient of pressure varies with Mach number by the relation given below: . This relation is reasonably accurate for 0. Directional or weathercock stability is concerned with the static stability of the airplane about the z axis. Just as in the case of longitudinal stability it is desirable that the aircraft should tend to return to an equilibrium condition when subjected to some form of yawing disturbance. For this the slope of the yawing moment curve must be positive.
An airplane possessing this mode of stability will always point towards the relative wind, hence the name weathercock stability. It is common practice to derive a fourth order characteristic equation to describe the longitudinal motion, and then factorize it approximately into a high frequency mode and a low frequency mode. The approach adopted here is using qualitative knowledge of aircraft behavior to simplify the equations from the outset, reaching the result by a more accessible route.
The two longitudinal motions modes are called the short period pitch oscillation SPPO , and the phugoid. A short input in control systems terminology an impulse in pitch generally via the elevator in a standard configuration fixed-wing aircraft will generally lead to overshoots about the trimmed condition. The transition is characterized by a damped simple harmonic motion about the new trim. There is very little change in the trajectory over the time it takes for the oscillation to damp out.
Generally this oscillation is high frequency hence short period and is damped over a period of a few seconds. A short, sharp pull back on the control column may be used, and will generally lead to oscillations about the new trim condition. If the oscillations are poorly damped the aircraft will take a long period of time to settle at the new condition, potentially leading to Pilot-induced oscillation.
If the short period mode is unstable it will generally be impossible for the pilot to safely control the aircraft for any period of time. This damped harmonic motion is called the short period pitch oscillation; it arises from the tendency of a stable aircraft to point in the general direction of flight. It is very similar in nature to the weathercock mode of missile or rocket configurations. The velocity vector is:. According to Newton's Second Law , the accelerations are proportional to the forces , so the forces in inertial axes are:.
But the forces are generated by the pressure distribution on the body, and are referred to the velocity vector. But the velocity wind axes set is not an inertial frame so we must resolve the fixed axes forces into wind axes. Also, we are only concerned with the force along the z-axis:. In words, the wind axes force is equal to the centripetal acceleration. The moment equation is the time derivative of the angular momentum :.
The equations of motion, with all forces and moments referred to wind axes are, therefore:. These are characterized by stability derivatives determined from the flight condition. The possible stability derivatives are:. Since the tail is operating in the flowfield of the wing, changes in the wing incidence cause changes in the downwash, but there is a delay for the change in wing flowfield to affect the tail lift, this is represented as a moment proportional to the rate of change of incidence:.
The damping term is reduced by the downwash effect, and it is difficult to design an aircraft with both rapid natural response and heavy damping. Usually, the response is underdamped but stable. Residual fourpack Arrangement of histogram of the residuals, normal probability plot of the residuals, residual versus fit plot, and residual versus order plot on one page.
View residual plots at the same time. Score plot Scatterplot of the x-scores from the first and second components. Display the overall arrangement of the data using the first two components to identify leverage points or clusters of points. Display the overall arrangement of the data using the first three components to identify leverage points or clusters of points. Loading plot Connected scatterplot of the x-loadings from the first and second components. Display the correlation between the loadings of each predictor on the first and second components.
Compare the importance of predictors to the model. Residual X plot Connected scatterplot of the x-residuals, in which each line represents an observation and has as many points as predictors.
Skip to Organizational Offices. Skip to Bottom Navigation. Author s : M. Sword Date: Source: Plant and Soil. Description In , two levels each of stand density and fertilization treatments were factorially established in a 9-year-old loblolly pine plantation on a P-deficient Gulf Coastal Plain site in Rapides Parish, Louisiana, USA.
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