A transportation problem uses Minimum radius for superelevation. Given design speed (V) = 60.0000 mph; superelevation rate (e) = 0.0500; side friction factor (f) = 0.1550, determine the minimum radius (R) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Minimum radius for superelevation.
• Everything except R is given, so isolate R symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Transportation items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = V^2 / (15 (e + f))$$

2. Step 2 — Rearrange the relation so that R stands alone on the left-hand side.

3. Step 3 — List the givens: design speed (V) = 60.0000 mph, superelevation rate (e) = 0.0500, side friction factor (f) = 0.1550.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$R = 1171\ \text{ft}$$

6. Step 6 — Check: returning R = 1,171 ft to

   $$R = V^2 / (15 (e + f))$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 2,341 — kept a factor of two that cancels in the correct rearrangement.
• 585.4 — dropped that same factor in the other direction.
• 1,288 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Transportation → Horizontal Curves

A transportation problem uses Minimum radius for superelevation. Given superelevation rate (e) = 0.0750; side friction factor (f) = 0.1400; minimum radius (R) = 1,288 ft, determine the design speed (V) in mph.

Start with the thinking

• The governing relation printed in this handbook section is Minimum radius for superelevation.
• Everything except V is given, so isolate V symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Transportation items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = V^2 / (15 (e + f))$$

2. Step 2 — Rearrange the relation so that V stands alone on the left-hand side.

3. Step 3 — List the givens: superelevation rate (e) = 0.0750, side friction factor (f) = 0.1400, minimum radius (R) = 1,288 ft.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$V = 64.4500\ \text{mph}$$

6. Step 6 — Check: returning V = 64.4500 mph to

   $$R = V^2 / (15 (e + f))$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 128.9 — kept a factor of two that cancels in the correct rearrangement.
• 32.2250 — dropped that same factor in the other direction.
• 70.8950 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Transportation → Horizontal Curves

A transportation problem uses Minimum radius for superelevation. Given design speed (V) = 50.0000 mph; side friction factor (f) = 0.1450; minimum radius (R) = 2,516 ft, determine the superelevation rate (e).

Start with the thinking

• The governing relation printed in this handbook section is Minimum radius for superelevation.
• Everything except e is given, so isolate e symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Transportation items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = V^2 / (15 (e + f))$$

2. Step 2 — Rearrange the relation so that e stands alone on the left-hand side.

3. Step 3 — List the givens: design speed (V) = 50.0000 mph, side friction factor (f) = 0.1450, minimum radius (R) = 2,516 ft.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$e = -0.0788$$

6. Step 6 — Check: returning e = -0.0788 to

   $$R = V^2 / (15 (e + f))$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• -0.1575 — kept a factor of two that cancels in the correct rearrangement.
• -0.0394 — dropped that same factor in the other direction.
• -0.0866 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Transportation → Horizontal Curves

A transportation problem uses Minimum radius for superelevation. Given design speed (V) = 50.0000 mph; superelevation rate (e) = 0.0950; side friction factor (f) = 0.1350, determine the minimum radius (R) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Minimum radius for superelevation.
• Everything except R is given, so isolate R symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Transportation items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = V^2 / (15 (e + f))$$

2. Step 2 — Rearrange the relation so that R stands alone on the left-hand side.

3. Step 3 — List the givens: design speed (V) = 50.0000 mph, superelevation rate (e) = 0.0950, side friction factor (f) = 0.1350.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$R = 724.6\ \text{ft}$$

6. Step 6 — Check: returning R = 724.6 ft to

   $$R = V^2 / (15 (e + f))$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 1,449 — kept a factor of two that cancels in the correct rearrangement.
• 362.3 — dropped that same factor in the other direction.
• 797.1 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Transportation → Horizontal Curves

A transportation problem uses Minimum radius for superelevation. Given superelevation rate (e) = 0.0850; side friction factor (f) = 0.1300; minimum radius (R) = 2,955 ft, determine the design speed (V) in mph.

Start with the thinking

• The governing relation printed in this handbook section is Minimum radius for superelevation.
• Everything except V is given, so isolate V symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Transportation items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = V^2 / (15 (e + f))$$

2. Step 2 — Rearrange the relation so that V stands alone on the left-hand side.

3. Step 3 — List the givens: superelevation rate (e) = 0.0850, side friction factor (f) = 0.1300, minimum radius (R) = 2,955 ft.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$V = 97.6211\ \text{mph}$$

6. Step 6 — Check: returning V = 97.6211 mph to

   $$R = V^2 / (15 (e + f))$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 195.2 — kept a factor of two that cancels in the correct rearrangement.
• 48.8105 — dropped that same factor in the other direction.
• 107.4 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Transportation → Horizontal Curves

A transportation problem uses Minimum radius for superelevation. Given design speed (V) = 20.0000 mph; side friction factor (f) = 0.1050; minimum radius (R) = 133.0 ft, determine the superelevation rate (e).

Start with the thinking

• The governing relation printed in this handbook section is Minimum radius for superelevation.
• Everything except e is given, so isolate e symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Transportation items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = V^2 / (15 (e + f))$$

2. Step 2 — Rearrange the relation so that e stands alone on the left-hand side.

3. Step 3 — List the givens: design speed (V) = 20.0000 mph, side friction factor (f) = 0.1050, minimum radius (R) = 133.0 ft.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$e = 0.0955$$

6. Step 6 — Check: returning e = 0.0955 to

   $$R = V^2 / (15 (e + f))$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 0.1910 — kept a factor of two that cancels in the correct rearrangement.
• 0.0478 — dropped that same factor in the other direction.
• 0.1051 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Transportation → Horizontal Curves

A transportation problem uses Minimum radius for superelevation. Given design speed (V) = 50.0000 mph; superelevation rate (e) = 0.0700; side friction factor (f) = 0.0950, determine the minimum radius (R) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Minimum radius for superelevation.
• Everything except R is given, so isolate R symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Transportation items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = V^2 / (15 (e + f))$$

2. Step 2 — Rearrange the relation so that R stands alone on the left-hand side.

3. Step 3 — List the givens: design speed (V) = 50.0000 mph, superelevation rate (e) = 0.0700, side friction factor (f) = 0.0950.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$R = 1010\ \text{ft}$$

6. Step 6 — Check: returning R = 1,010 ft to

   $$R = V^2 / (15 (e + f))$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 2,020 — kept a factor of two that cancels in the correct rearrangement.
• 505.1 — dropped that same factor in the other direction.
• 1,111 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Transportation → Horizontal Curves

A transportation problem uses Minimum radius for superelevation. Given superelevation rate (e) = 0.0900; side friction factor (f) = 0.1050; minimum radius (R) = 1,615 ft, determine the design speed (V) in mph.

Start with the thinking

• The governing relation printed in this handbook section is Minimum radius for superelevation.
• Everything except V is given, so isolate V symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Transportation items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = V^2 / (15 (e + f))$$

2. Step 2 — Rearrange the relation so that V stands alone on the left-hand side.

3. Step 3 — List the givens: superelevation rate (e) = 0.0900, side friction factor (f) = 0.1050, minimum radius (R) = 1,615 ft.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$V = 68.7305\ \text{mph}$$

6. Step 6 — Check: returning V = 68.7305 mph to

   $$R = V^2 / (15 (e + f))$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 137.5 — kept a factor of two that cancels in the correct rearrangement.
• 34.3652 — dropped that same factor in the other direction.
• 75.6035 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Transportation → Horizontal Curves

A transportation problem uses Minimum radius for superelevation. Given design speed (V) = 35.0000 mph; side friction factor (f) = 0.1650; minimum radius (R) = 2,720 ft, determine the superelevation rate (e).

Start with the thinking

• The governing relation printed in this handbook section is Minimum radius for superelevation.
• Everything except e is given, so isolate e symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Transportation items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = V^2 / (15 (e + f))$$

2. Step 2 — Rearrange the relation so that e stands alone on the left-hand side.

3. Step 3 — List the givens: design speed (V) = 35.0000 mph, side friction factor (f) = 0.1650, minimum radius (R) = 2,720 ft.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$e = -0.1350$$

6. Step 6 — Check: returning e = -0.1350 to

   $$R = V^2 / (15 (e + f))$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• -0.2700 — kept a factor of two that cancels in the correct rearrangement.
• -0.0675 — dropped that same factor in the other direction.
• -0.1485 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Transportation → Horizontal Curves

A transportation problem uses Minimum radius for superelevation. Given design speed (V) = 60.0000 mph; superelevation rate (e) = 0.1000; side friction factor (f) = 0.1450, determine the minimum radius (R) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Minimum radius for superelevation.
• Everything except R is given, so isolate R symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Transportation items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = V^2 / (15 (e + f))$$

2. Step 2 — Rearrange the relation so that R stands alone on the left-hand side.

3. Step 3 — List the givens: design speed (V) = 60.0000 mph, superelevation rate (e) = 0.1000, side friction factor (f) = 0.1450.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$R = 979.6\ \text{ft}$$

6. Step 6 — Check: returning R = 979.6 ft to

   $$R = V^2 / (15 (e + f))$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 1,959 — kept a factor of two that cancels in the correct rearrangement.
• 489.8 — dropped that same factor in the other direction.
• 1,078 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Transportation → Horizontal Curves