Offtracking Simulation Dating -

Offtracking Simulation Dating

offtracking simulation dating

Erkert In partial oftfracking of the requirements for the degree of: Master of Science Presented to: Department of Civil Engineering Oregon State University Corvallis, Oregon June ifftracking Abstract Offtracking simulation dating of the analytical techniques that are currently available are not capable of analyzing the offtracking of truck and trailer combinations or the path of load overhangs through a set of curves that are commonly found on forest roads. Advances in 24 dating 47 processing speed of microcomputers have made it possible to simulate how a truck and trailer combination negotiate a road. Offtracking simulation dating program will enable road designers to predict offtracking through a complex set of road geometrics, including compound and reverse curves.

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The following briefly discusses each method and the advantages and disadvantages of each, For a full discussion of any particular method, the reader should review the referenced literature Direct Solution of Maximum Offtracking The best known method for the direct solution of maximum offtracking is that of the equations in the Society of Automotive Engineers Handbook [14].

These equations are commonly known as the "Sum of the Squares of Wheelbases". The principle behind the equation is shown in Figure The maximum offtracking is obtained when a projected line through the centerline of a trailing axle intersects the radius point of the curve.

Sum of the Squares of the Wheelbases The maximum offtracking OT of the vehicle combination in Figure relative to the longitudinal centerline of the vehicle can be solved for as: The main advantage of this approach is that any vehicle configuration can be analyzed fairly quickly.

The disadvantages are: Not valid for curves that are not long enough for the vehicle combination to develop maximum offtracking. Not capable of analyzing transitional wheel paths.

Many curves are not long enough for maximum offiracking to develop, The path that the rear wheels follow up to maximum offtracking is called the transitional wheel path. Not capable of analyzing compound and reverse curves. The shortcomings of this approach has lead to an empirical approach that is discussed next Empirical Methods The USDA Forest Service developed an empirical method to predict offiracking from the sum of the squares of the wheelbases and to take into account curves that are not long enough to develop maximum offiracking [ The technique used a regression equation based on the sum of the squares of the wheelbases and modified it to take account of the curve central angle.

The regression equation was developed from charts that were produced from a set of tractrix equations published by the San Dimas Equipment Development Center [3. The regression equation was tested with a field test on a log truck and a scale model simulator for a lowboy vehicle combination [10]. The equation reported is: It is used in the form of design charts that give the required road width for a standard log truck and lowboy for radii of 50 to feet and central angles of 10 to degrees.

A two foot steering correction is added to the result of the regression equation within the design charts. The advantages to using this approach are that it is quick, easy to use, and relatively accurate. However, it is only valid for one simple curve with long tangents at each end of the curve. Not capable of analyzing a load overhang path.

Not capable of analyzing compound and reverse curves Scale Models Because of the deficiencies of the previous methods, scale model simulators have been used to analyze offtracking of vehicle combinations through a set of curves.

There are three scale models that have been developed, U. Each of the scale models are slightly different but are used with the following procedure: The road traverse is drawn to a large scale. The model is adjusted to the dimensions of the vehicle unit or combination. The model is carefully guided over the traverse drawing and a set of pens trace the paths of the rear most wheels.

The scale models have been found to be fairly accurate when compared to field tests of actual equipthent [10], The DVS is probably the most useful of the scale models for forest road designers. It is capable of analyzing four different vehicle combinations directly. It will also plot the path of a load overhang for a down rigged yarder tower on a rubber tired undercarriage.

The disadvantages of the scale models are that they are somewhat cumbersome to use for designing road sections of any length Field Simulators Several field vehicle simulators have been designed by the USDA Forest Service for analyzing offtracking of a single unit or a two unit vehicle combination on existing roads.

These models are constructed out of light weight aluminum tubing and are adjustable in length to simulate different wheelbases. No published results of the accuracy of these models exist in the literature to date. However, these simulators have proven to be quite useful in practice and are felt to be fairly accurate.

The 12 21 disadvantages of these are: Only a single unit vehicle and a tractor-trailer type vehicle are available. The tee hnique is of course not applicable to new construction design work Computer Simulation Four computer simulation techniques have been developed from Two of the techniques are not applicable to the forest environment as they were developed to look specifically at problems in urban intersection design [1, 4].

The remaining two techniques use very different approaches to the problem. The two techniques are summarized as follows: Tractrix Alprithm There exists a general mathematical description of the path that the rear of a vehicle follows from a given input steering curve. A steering curve is defined as the set of geometrics that guide the leading vehicle in a vehicle combination.

The steering curve can be defined as circular or a straight line. The path of the trailing axle is known as the general tractrix of the original steering curve [6]. To find a closed form solution, the differential equations must be integrated. This process is extremely complex and not suited for general practice [12]. In , Leonard Della-Moretta of the USDA Forest Service, derived a simplified set of the original equations for a single unit vehicle that could be programmed on a computer [3].

Unfortunately, the program and the algorithm were never fully developed for combination vehicles, The differential iracthx equations are the basis of the OFFTRACK program. In this algorithm, a series of geometric relationships were derived to describe the spiral path of the trailing vehicle unit. The centerline of the front axle of the first vehicle unit in the combination is moved along the steering curve in one foot increments.

The approach can be done by hand but is of course too laboribus for practical use. The general procedure is to: Extend a line towards the center of the curve along the path of the rear axle of the unit. Extend,a line from the centerline of the front axle on the steering curve through the center of rotation of the steering curve.

The point of intersection of the. Move the centerline of the front axle along the steering curve a distance of one foot. Strike an arc from the new front axle location across the path of the centerline of the rear axle. The arc has a radius equal to the wheelbase of the vehicle unit. Strike an arc from the center of rotation of the rear axle across the arc from step 3. The arc has a radius equal to the distance from the center of rotation of the rear axle to the centerline of the rear axle in it's previous 14 23 location.

The point of intersection of the arc's in step 3 and step 4 is the new location of the centerline of the rear axle. This completes the cycle of one movement, return to step I and continue. The computer program uses a set of equations to accomplish the same set of steps above but for multi-unit vehicles. An absolute coordinate system is used to keep track of the vehicle locations.

The main advantages of the program is that it is capable of analyzing any vehicle configuration and will plot the swept path of the outside front wheel and the inside rear wheel.

The disadvantages of the program are: It is slow to execute. It takes from several minutes to 20 minutes to compute the paths for a single curve. Plotting is done on a dot matrix printer which takes another 5 to 15 minutes.

The plot is done in four pieces and must be taped together [12]. No direct output of the required road widths is available. The dot matrix plot must be done and the widths scaled off of the plot. The analysis is only accomplished in one direction. Forest roads are usually terminal facilities that the vehicle must drive in, remove the load, and drive back out.

The program is currently not capable of analyzing load overhang paths. It corrects most of the disadvantages of the currently available techniques discussed in section 2. It is programmed for the IBM and compatible family of computers. The tractrix algorithm is used as the method for describing how a vehicle negotiates a given road [3].

Much development work was done in linking multi-unit vehicles together as the original algorithm was for a single unit vehicle. The theory behind the program is not presented here but is discussed in other articles by the authors [16] Objectives The OFFTRACK program was designed to be a production tool to enable forest road designers to determine quickly and accurately required road widths andload overhang paths. The following objectives were established: Easy to use with a simple user interface.

Capable of analyzing offiracking through a complex set of geometrics. Capable of analyzing offtracking both ahead and back automatically. Capable of analyzing load overhang paths. Capable of determining required road widths left and right of centerline directly. Capable of analyzing most of the vehicle combinations found on forest roads.

Accurate and execute quickly. Provide the user with a graphical display of the wheel and load paths to promote understanding of the numeric results Program Features The program features a pull down menu structure and on line help for ease of use. An Overview cognitive radio and game theory overview simulation dating In August The suspected belly is emerging economic status. In this work quantum games to quantum wireless networks [6, 7], in order to enhance cites [11, 12], a quantum formulation of the dating market problem was intro- duced Simulation Results 1 1 Keywords: Ask My man checked the compatibility of questions, making cMatch a prayer warrior?

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