Excerpt

## ABSTRACT

In some countries, there is very little standardization in the construction of speed-bumps (aka. speed-breakers), as a result of which the bottom of many cars scrape the speed- bumps. In this paper, we come up with a first order figure of merit that car manufacturers can use when adapting their cars to be sold in such countries, so as to minimize the chances of scraping the speed-bumps.

Keywords: Bottom, Car, Ground-clearance, Scrape, Speed-bump, Wheel-base Nomenclature

L : Length of speed-bump, mm

h : Peak height of speed-bump, mm

g : Ground-clearance of vehicle, mm

w : Wheel-base of vehicle, mm

r : Radius of the wheels, mm

## 1. Introduction

In some developing countries, there is very little standardization in the construction of speed-bumps (aka. speed-breakers). The height and profile of the speed-bumps are very non-standard, as a result of which the bottom of many cars scrape the speed-bumps. This is a safety concern because such repeated impacts to a monocoque structure can cause damage to the body shell, besides resulting in an unpleasant driving experience. This is especially a problem for international car manufacturers who wish to sell their cars in that country. In this paper, we come up with a first order model for the figure of merit that car manufacturers can use when adapting their cars to be sold in such countries, so as to minimize the chances of scraping the speed-bumps. Car buyers can also use this model to evaluate one car versus another, as regards susceptibility to scrape speed-bumps.

Contrary to conventional belief, ground-clearance alone is not a criterion for scrape-susceptibility. The wheel-base also plays a role, especially for long speed-bumps. Indeed, if the length of the speed-bump is longer than the vehicle’s wheel-base, then the ground-clearance requirements of the vehicle can often be relaxed, which is a desirable goal for manufacturers to get better vehicle dynamics from a stability and ride/handling point of view.

In this paper, we develop a model that shows the inter-play between the ground- clearance and the wheel-base. We develop the model in section 2, and we present the results in Section 3.

## 2. Model

Non-standard speed-bumps come in varying profiles, as seen in Fig. 1. It is very difficult to model scrape-susceptibility for all the various profiles. Hence, as a first order model, we develop the model for a simple isosceles triangular profile shown in Fig. 1b.

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Fig. 1: Profiles of various speed-bumps.

Consider a vehicle negotiating such a speed-bump. It is clear that if the speed-bump is short enough (L < w), then the ground-clearance has to be greater than the speed-bump’s height (g > h). This is the trivial case. But most often, speed-bumps are longer and have a smoother up-ramp and down-ramp. Because of this, when the front wheels have crossed the peak of the speed-bump but before they completely cross the speed-bump, the rear wheels start climbing the up-ramp. This raises the height of the lowest point of the vehicle’s bottom, and hence reduces the chances of scraping the speed-bump. This is the reason why the ground-clearance requirements can be relaxed when the wheel-base is shorter than the speed-bump’s length. This is the non-trivial case, and this is what we model in the next section.

### 2.1. Model Formulation

Fig. 2 shows the situation described above, at the point when the rear wheel is just about to start the up-ramp and the bottom is about to scrape the speed-bump.

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Fig. 2: Vehicle navigating a speed-bump, traveling right to left.

By formulating a model for this condition, we would have essentially formulated a condition to prevent scraping. It should be noted however that this would be a necessary condition and not a sufficient condition to prevent scraping. As the rear wheels climb the up-ramp, the front wheels descend the down-ramp. Depending on whether the descent is greater or the ascent is greater, a sufficient condition may be derived. But that is left for a future work.

Consider Fig. 3 which is a detailed view of the rear wheel. Line DE represents the bottom of the vehicle. Using elementary geometric relations, we can see that:

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Using the SINE rule in triangle PEO, we can see that:

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Fig. 3: Analysis of the rear wheels (right end of figure)

In triangle BPC, we can see that:

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Elimination OP in (2) and (3), we get:

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Let us analyze the situation at the front wheel now. Consider Fig. 4 which is a detailed view of the front wheel.

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Fig. 4. Analysis of the front wheels (left end of figure)

In triangle BQD, we can see that:

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**[...]**

- Quote paper
- Venkatnarayan Hariharan (Author), 2017, Design considerations for ground-clearance and wheel-base for navigating non-standard speed-bumps, Munich, GRIN Verlag, https://www.grin.com/document/358591

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