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Or, the low-tech approach (Mechanical skills required: the ability to bang nails, or apply duct tape). Build a simple rectangular frame high enough and wide enough to fit around the widest/tallest points of your vehicle. Calculate the area of the enclosed rectangle. Take a series of measurements of the gap between your vehicle and the frame (the more measurements you take, the more accurate your result). From there it's relatively simple to calculate the difference by various means, either by 'filling in' the space with progressively smaller cubes, or by creating an analog in a drawing programme.
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