A 490 ft equal-tangent sag curve is currently designed for 50 mph. A CE 321 student thinks that traveling at 55 mph on the curve is safe for a van since the van will have a higher headlight height. If the all other design inputs are standard, what must the driver's eye height be (in the van) for the student's claim to be valid?
A 490 ft equal-tangent sag curve is currently designed for 50 mph. A CE 321 student thinks that traveling at 55 mph on the curve is safe for a van since the van will have a higher headlight height. If the all other design inputs are standard, what must the driver's eye height be (in the van) for the student's claim to be valid?
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![### Example Problem: Sag Curve Design
---
#### Given:
- \( V = 50 \ \text{mph} \)
- \( L = 510'\ \text{sag curve} \)
---
#### Find:
- \( H_1 \) for \( V = 55 \ \text{mph} \)
---
#### Solution:
1. **From Table 3.2**:
\[
K_{\text{design}} (50 \ \text{mph}) = 96
\]
2. **Compute \( A \)**:
\[
L = K \times A \implies A = \frac{L}{K} = \frac{510}{96} = 5.3
\]
3. **Assume \( S \leq L \)**
4. **From Table 3.1**:
\[
S (55 \ \text{mph}) = 495'
\]
5. **Since \( 495' < 510' \)** the assumption is okay.
6. **Calculation using the formula**:
\[
L = \frac{AS^2}{800(H_c - \frac{(H_1 + H_2)}{2})} \implies 510 = 5.3 \times \frac{495^2}{800(16.5 - \frac{(H_1 + 2)}{2})}
\]
7. **Standard values**:
\[
(H_c = 16.5, \ H_2 = 2 \ \text{is design standard})
\]
8. **Solving for \( H_1 \)**:
\[
H_1 = 24.6 \ \text{ft}
\]
---
This page explains how to determine the height of an obstruction ( \( H_1 \) ) for a sag curve at a given speed by using the provided design standard tables and performing the necessary calculations. The steps involve deriving the acceleration value \( A \), verifying the length assumption, and solving the formula to find \( H_1 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb2d7e9b1-7208-47e7-acf1-5a4d04c3ff3b%2F674efc1e-79c8-4e75-ab8d-87b2788b832f%2Ffkevlx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Example Problem: Sag Curve Design
---
#### Given:
- \( V = 50 \ \text{mph} \)
- \( L = 510'\ \text{sag curve} \)
---
#### Find:
- \( H_1 \) for \( V = 55 \ \text{mph} \)
---
#### Solution:
1. **From Table 3.2**:
\[
K_{\text{design}} (50 \ \text{mph}) = 96
\]
2. **Compute \( A \)**:
\[
L = K \times A \implies A = \frac{L}{K} = \frac{510}{96} = 5.3
\]
3. **Assume \( S \leq L \)**
4. **From Table 3.1**:
\[
S (55 \ \text{mph}) = 495'
\]
5. **Since \( 495' < 510' \)** the assumption is okay.
6. **Calculation using the formula**:
\[
L = \frac{AS^2}{800(H_c - \frac{(H_1 + H_2)}{2})} \implies 510 = 5.3 \times \frac{495^2}{800(16.5 - \frac{(H_1 + 2)}{2})}
\]
7. **Standard values**:
\[
(H_c = 16.5, \ H_2 = 2 \ \text{is design standard})
\]
8. **Solving for \( H_1 \)**:
\[
H_1 = 24.6 \ \text{ft}
\]
---
This page explains how to determine the height of an obstruction ( \( H_1 \) ) for a sag curve at a given speed by using the provided design standard tables and performing the necessary calculations. The steps involve deriving the acceleration value \( A \), verifying the length assumption, and solving the formula to find \( H_1 \).
Transcribed Image Text:### Design of Equal-Tangent Sag Curves: Considerations for Headlight Height
#### Problem Statement:
**Given:**
- A 490 ft equal-tangent sag curve is currently designed for 50 mph.
- A student from CE 321 suggests that traveling at 55 mph on the curve is safe for a van with a higher headlight height.
**Question:**
- If all other design parameters are standard, what must the driver's eye height be (in the van) to support the student's claim?
**Example Problem:**
- A 510 ft equal-tangent sag curve is currently designed for 50 mph.
- A CE 321 student believes that traveling at 55 mph on the curve is safe for a van because the van has a higher headlight height.
**Question in Example:**
- What must the driver's eye height be (in the van) for the student’s belief to be valid, assuming all other design inputs are standard?
### Explanation:
This problem revolves around the design of equal-tangent sag curves and the impact of vehicle headlight height on safe traveling speeds. When curves are designed, one critical aspect is ensuring that drivers can see far enough ahead to stop safely if necessary.
**Key Concepts:**
1. **Sag Curve:** A vertical curve where the initial slope is descending and then ascending, forming a ‘sag’ in the road.
2. **Design Speed:** The speed at which the curve is originally designed to be safely traversed.
3. **Headlight Height:** The height at which headlights project light on the road, which influences the driver's visibility.
**Considerations:**
- The equation to determine the minimum radius or length of the sag curve often includes terms for headlight height and reaction time.
- If the headlight height increases, the distance the light projects also increases, leading to better visibility and potentially allowing for higher speeds.
The original and example problems require recalculating the curve design with the new headlight height to verify the claim. Assuming standard inputs such as:
- Perception-reaction time.
- Coefficient of friction.
- Deceleration rate.
These a well-known parameters in road design can be used in conjunction with the given headlight height to find the required adjustments for safety at different speeds.
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