Forward speed

Assume that a mathematical model for a motor vehicle is required, relating the accelerator pedal angle 6 to the forward speed u, a simple mathematical model might be... 

Fig. 2.1 Vehicle forward speed plotted against accelerator angle.

If the constants b, c and d were not available, then the vehicle model could be obtained by measuring the forward speed u t) for a number of different accelerator angles 6 t) and plotting the results, as shown in Figure 2.1. 

Equation (2.1) for the motor vehicle implies that when there is a change in accelerator angle, there is an instantaneous change in vehicle forward speed. As all car drivers know, it takes time to build up to the new forward speed, so to model the dynamic characteristics of the vehicle accurately, this needs to be taken into account. 

For braking Vf > Vs is positive and has a maximum value of 1. For acceleration Vf < Vs is negative and becomes infinite when the forward speed is zero, i.e., the driven wheel spins through. 

V is the forward speed of the abrasive disk in the contact area relative to the sample wheel... 

Tips Stay low and on your hands, elbows, and knees. Keep your head up and looking forward. Speed is not as crucial as not falling through the gaps. 

Consider again the TST rate expression (14.12) for a reaction a b, and assume that the assumptions underlying TST hold except that for a particle that crosses the transition point tb with forward speed v (direction a —> b) there is a finite probability Pi,. < a(v) to endup in state b. In this case expression (14.12) should be modified to read... 

The most commonly used application systems in arable crops are boom sprayers equipped with equally spaced hydraulic nozzles (Robinson, 1993). The quality of the spray influences the quantity deposited on the crop and spray-drift. The combination of forward speed, nozzle type and pressure defines the sprayed volume. Volume rates have been reducing for several decades. While in the 1950s it was common to spray 10001/ha, nowadays 100-3001/ha is more common. 

Agricultural crop sprayers employ one of two methods for controlling the dose of a spraying system travelling at a defined or measured forward speed, namely ... 

Many of the larger sizes of boom sprayer used to treat arable crops in Northern European conditions have a control system that adjusts the volume output rate depending upon measured forward speed, so as to keep the delivered dose constant over a range of operating speeds. 

Since flow rate is proportional to the square root of pressure (e.g. to double the flow rate requires a fourfold increase in pressure), the range over which such control strategies can be operated effectively is commonly limited to a nominal value of 25% (Paice et al., 1996). While this range is often adequate to compensate for changes in forward speed due to differences, for example, in field terrain, it is not adequate for making spatially variable applications of plant-protection products. 

The initial development of either volume-based or injection metering dose-control systems aimed at achieving a uniform controlled dose across a treatment area that was independent of machine variables, particularly forward speed. However, there is substantial evidence to show that the target requirements for many plant-protection products are not uniform across a field, and that there is the... 

If flight forward speeds are low, the main rotor may contribute to greater crop penetration... 

The bond graph of the full model is also given in Fig. 2.5 and has six ideal energy elements, two of each type (/, C, and / ), and their parameters are given in Table 2.1. Note that the model includes only the system dynamics in the vertical direction the constant forward speed is used only to convert the spatial road description Zr x) into a temporal vertical velocity input, Vr(t), at the road/tire interface as shown in... 

Fig. 2.6. The vehicle is assumed to be traveling at a constant forward speed Vp on a flat road and at some point jc = JCo it reaches a smooth curb. The transition of the road profile from low to high level (Z = 0.2 m) is described by a cycloid function, whereas the length of the curb is L = 0.5 m.

This illustrative example is divided into three studies. The first study explores the proposed model reduction procedure by showing the outputs of many of the intermediate steps leading to the proper model for a single high forward speed input. Because the proper model is scenario dependent, a second study explores the effect of changing the input to a smoother input (lower vehicle forward speed than that used in the first study) on the proper model produced. Finally, a third study explores the effect of the user-defined model reduction threshold, (/ ), on the reduced model accuracy, by generating a series of reduced models under the same input conditions. 

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