Tractive Effort and Train Resistance

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Questions and Answers

What is the formula for calculating force as described in the content?

  • Force = Energy / Distance
  • Force = Speed / Energy
  • Force = Power / Speed
  • Force = Mass x Acceleration (correct)

How does tractive effort (TE) behave in the speed range of 0 to 20 mph?

  • TE increases at an accelerating rate
  • TE is variable and unpredictable
  • TE decreases monotonically with speed
  • TE is constant (correct)

What is the relationship between power, force, and speed?

  • Power = Force + Speed
  • Power = Force x (Distance / Time) (correct)
  • Power = Force / Speed
  • Power = Speed / Force

What is the maximum tractive effort (TE) value described in the example?

<p>100 kN (B)</p> Signup and view all the answers

How is energy consumed in moving an object defined?

<p>Energy = Force x Distance (C)</p> Signup and view all the answers

What happens to acceleration as speed increases beyond 20 mph according to the content?

<p>Acceleration begins to decrease (C)</p> Signup and view all the answers

How do you convert speed from mph to m/s as demonstrated in the example?

<p>Divide by 2.2 (D)</p> Signup and view all the answers

What is the calculated power at a speed of 20 mph with a maximum TE of 100 kN?

<p>910 kW (B)</p> Signup and view all the answers

What is the Maximum Power at Rail primarily focused on?

<p>Power needed to actually move the train (A)</p> Signup and view all the answers

What characterizes Continuous Tractive Effort?

<p>Power maintained during continuous motion (C)</p> Signup and view all the answers

What is the purpose of 'back emf' in a DC motor?

<p>To oppose the applied voltage (C)</p> Signup and view all the answers

How is Starting Tractive Effort defined?

<p>Effort required to start moving from a stop (A)</p> Signup and view all the answers

What limits the Short Term Tractive Effort?

<p>Overheating of traction motors and transmission (D)</p> Signup and view all the answers

Which factors can influence Continuous Power rating?

<p>Equipment characteristic and time proportions (A)</p> Signup and view all the answers

Why does the total power drawn from the supply exceed 910kW?

<p>Because of auxiliary loads and conversion losses (B)</p> Signup and view all the answers

How long can Short Term Tractive Effort typically be sustained?

<p>For a prescribed short period of time (A)</p> Signup and view all the answers

What happens to the maximum power curve at speeds over 70 mph?

<p>It dips noticeably (D)</p> Signup and view all the answers

Which component is NOT a part of the calculation for Tractive Effort?

<p>Horsepower (A)</p> Signup and view all the answers

What happens to the torque when the motor speeds up and the internally generated voltage rises?

<p>The torque falls. (B)</p> Signup and view all the answers

What is the Balancing Condition in relation to train acceleration?

<p>When the torque produced by the motors matches train resistance. (A)</p> Signup and view all the answers

What does the specific resistance 'R' during a run depend on?

<p>The static and dynamic factors of the train. (B)</p> Signup and view all the answers

In the train resistance formula, what does the term 'cv^2' represent?

<p>Air resistance. (C)</p> Signup and view all the answers

How is the tractive effort (TE) required to start a train calculated?

<p>By summing the resistance of the load, loco, and train weights. (D)</p> Signup and view all the answers

What does the variable 'a' represent in the train resistance formula?

<p>Static friction. (A)</p> Signup and view all the answers

Which of the following is NOT a factor contributing to train resistance during a run?

<p>Resistance due to atmospheric pressure. (D)</p> Signup and view all the answers

Which of these states accounts for resistance to start a train on straight level track?

<p>Static resistance. (D)</p> Signup and view all the answers

If the drag of the train increases with speed, what effect does this have on the effective torque?

<p>It decreases the effective torque. (A)</p> Signup and view all the answers

What does 'TE' stand for in the context of train operation?

<p>Tractive Effort. (D)</p> Signup and view all the answers

What happens to the balancing speed of a train on an up-gradient compared to level ground?

<p>It decreases. (A)</p> Signup and view all the answers

How is the tractive effort required to overcome curve-resistance determined?

<p>By weight and speed of the train. (C)</p> Signup and view all the answers

What is the effect of increasing gear ratio on a locomotive's performance?

<p>It allows for higher starting tractive effort. (C)</p> Signup and view all the answers

What change occurs in tractive effort as wheel diameter decreases?

<p>Starting tractive effort increases. (D)</p> Signup and view all the answers

How does field shunting affect a DC motor's operation?

<p>It enables the motor to run faster than its balancing speed. (B)</p> Signup and view all the answers

What is the formula for calculating the running resistance of a train at a given speed 'V' for a BOXN load?

<p>T1 = 0.6438797 + 0.01047218 V + 0.00007323 V² (D)</p> Signup and view all the answers

How does the gravitational force acting on a 150 tonne train calculate?

<p>Force = 150 x 1000 x 9.8 (D)</p> Signup and view all the answers

What is the resistance due to gravity for a train on a gradient of 1 in 200?

<p>7.3575 kN (D)</p> Signup and view all the answers

For a given gradient 'G', how is Specific Grade Resistance expressed?

<p>Specific Grade Resistance = (1/G) in kg/t (A)</p> Signup and view all the answers

What components remain unchanged when calculating running resistance of a train as it runs?

<p>T3 and T4 (C)</p> Signup and view all the answers

What is the effective voltage governed by in relation to train drag and resistance?

<p>By the torque of the motor (D)</p> Signup and view all the answers

What happens when the train starts to climb a grade and the speed reduces?

<p>Back voltage increases (D)</p> Signup and view all the answers

Which of the following correctly describes the relationship between Tractive Effort (TE) and overall train resistance?

<p>TE must be greater than overall train resistance to accelerate (A)</p> Signup and view all the answers

What modifies the effective voltage available to the motor during train operation?

<p>The drag force acting against the train (A)</p> Signup and view all the answers

What is the starting resistance of a loco expressed in kg/ton?

<p>6 kg/ton (B)</p> Signup and view all the answers

What happens to the tractive effort as speed increases beyond the 20 mph mark?

<p>Tractive effort falls as speed increases. (D)</p> Signup and view all the answers

How is power calculated when given a force and speed?

<p>Power = Force x Speed (B)</p> Signup and view all the answers

Which of the following best describes the relationship between mass, acceleration, and tractive effort?

<p>Tractive effort is directly proportional to mass and acceleration. (D)</p> Signup and view all the answers

At what point does maximum tractive effort occur based on the content?

<p>Between speeds of 0 and 20 mph. (A)</p> Signup and view all the answers

How is energy defined in the context of moving an object?

<p>Energy is the product of force and distance. (C)</p> Signup and view all the answers

What unit is used to express the maximum tractive effort in the example provided?

<p>kN (A)</p> Signup and view all the answers

Which statement correctly describes the relationship of speed and power at the rail?

<p>Power is the product of force and speed, limited by tractive effort. (A)</p> Signup and view all the answers

What happens to acceleration when tractive effort decreases with increasing speed?

<p>Acceleration decreases, leading to slower speed buildup. (A)</p> Signup and view all the answers

How does a reduction in gear ratio affect the locomotive's operational characteristics?

<p>Increases starting torque while reducing maximum operational speed. (C), Increases maximum operational speed but can lead to mechanical failure. (D)</p> Signup and view all the answers

What is the impact of wheel diameter reduction on tractive effort at different speeds?

<p>Increases tractive effort at lower speeds but reduces it at higher speeds. (D)</p> Signup and view all the answers

Which statement accurately describes the effect of field shunting on a DC motor's operation?

<p>Weakens the motor field, allowing for increased speed at the expense of torque. (B)</p> Signup and view all the answers

What occurs to the torque as the motor accelerates and the internally generated voltage increases?

<p>Torque decreases due to reduced current. (B)</p> Signup and view all the answers

Which statement best defines the balancing condition for a train?

<p>It is when the torque produced matches the train’s resistance. (B)</p> Signup and view all the answers

What is the significance of curvature resistance calculated using the formula TC = 0.4 X S X W?

<p>It indicates the resistance force acting against the forward motion of the train on a curve. (C)</p> Signup and view all the answers

How does one define Continuous Tractive Effort in relation to train operation?

<p>The tractive effort required to maintain train motion consistently without slipping. (B)</p> Signup and view all the answers

In the formula for train resistance, what does the variable 'b' specifically represent?

<p>Resistance due to mechanical factors. (C)</p> Signup and view all the answers

What specifically does a gearbox do in relation to the traction motors and train axles?

<p>Adjusts the motor speed to match the required axle speed for effective traction. (D)</p> Signup and view all the answers

What primarily affects the Continuous Power rating of equipment?

<p>The equipment characteristic and operational assumptions. (A)</p> Signup and view all the answers

What is the principal component expressed by 'a' in the train resistance formula?

<p>Static friction while starting the train. (A)</p> Signup and view all the answers

How is the effective voltage available to the motor primarily determined?

<p>By the resistance offered by the train. (A)</p> Signup and view all the answers

What limits the Short Term Tractive Effort when attempting to climb a grade?

<p>Overheating of traction motors and transmission equipment. (C)</p> Signup and view all the answers

Which of the following statements best describes Maximum Power at Rail?

<p>It represents the peak power needed for train acceleration. (A)</p> Signup and view all the answers

Which scenario best describes the impact of increasing the motor notches?

<p>It temporarily increases effective voltage and torque. (D)</p> Signup and view all the answers

What does the term 'cv^2' in the train resistance formula indicate?

<p>Air resistance proportional to the square of speed. (B)</p> Signup and view all the answers

What is the relationship between starting tractive effort and the locomotive's weight?

<p>Starting tractive effort is proportional to the loco weight multiplied by adhesion. (A)</p> Signup and view all the answers

Which statement accurately describes the existence of train resistance?

<p>It applies regardless of speed or gradient. (B)</p> Signup and view all the answers

What happens to the power curve of the equipment at speeds exceeding 70 mph?

<p>It shows a dip indicating decreased efficiency. (D)</p> Signup and view all the answers

What does 'back emf' in a DC motor primarily counteract during operation?

<p>The externally applied voltage. (A)</p> Signup and view all the answers

What is the influence of gradient on train resistance according to the context?

<p>Gradient contributes additional resistance when climbing uphill. (A)</p> Signup and view all the answers

Which of the following statements is true regarding the tractive effort required to start a train?

<p>It varies based on the operational gradient and curvature. (D)</p> Signup and view all the answers

Which parameter is NOT included when computing Tractive Effort?

<p>Speed of the train (B)</p> Signup and view all the answers

What is primarily considered when estimating Continuous Power in traction systems?

<p>The time spent coasting at lower tractive efforts. (A)</p> Signup and view all the answers

What effect does the increase in speed generally have on tractive effort needed?

<p>Tractive effort may increase due to resistance. (B)</p> Signup and view all the answers

What is the formula used to calculate the running resistance of a train at speed 'V' for a locomotive?

<p>T1 = 0.6438797 + 0.01047218 V + 0.00007323 V2 (A)</p> Signup and view all the answers

How is the tractive effort (TE) required to overcome a gradient of '1 in G' calculated for a train of weight 'W'?

<p>TG = W / G (D)</p> Signup and view all the answers

What is the approximate gravitational force acting on a 150 tonne train?

<p>1,471,500 N (D)</p> Signup and view all the answers

If a train climbs a 1 in 200 gradient, what is the resistance due to gravity?

<p>7.3575 kN (A)</p> Signup and view all the answers

For a loco, how is the second term of the running resistance formula influenced during operation?

<p>It increases linearly with speed. (A)</p> Signup and view all the answers

What component remains unchanged when calculating the running resistance of a train at a constant speed?

<p>Curve Resistance (T4) (A)</p> Signup and view all the answers

Which term in calculating running resistance describes the contribution of speed squared?

<p>0.00007323 V2 (A)</p> Signup and view all the answers

When speed reduces due to a train climbing a grade, what effect does this have on the back voltage?

<p>The back voltage decreases. (C)</p> Signup and view all the answers

What is the term used to describe the resistance experienced by a train moving on a gradient of '1 in 1'?

<p>Full Gravitational Resistance (C)</p> Signup and view all the answers

Flashcards

Tractive Effort (TE)

The force applied to the rails by a train's wheels to move it.

Force

The application of a push or pull that can cause an object to accelerate.

Energy

The amount of work done to move an object over a distance.

Power

The rate at which energy is used or produced.

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Maximum Tractive Effort

The greatest force a train's engine can produce at lower speeds.

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Power Calculation

Power = Force x Speed

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Relationship between Speed and Tractive Effort

Tractive Effort (TE) changes with speed. It's usually high at lower speeds, and decreases at higher speeds.

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Power Calculation (Example)

Power is calculated by multiplying the force and the speed values.

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Maximum Power at Rail

The power needed to move a train.

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Continuous Power Rating

The power a train can consistently produce over a period of time.

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Starting Tractive Effort

The power needed to start moving a stationary train.

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Continuous Tractive Effort

Power needed to keep a train moving continuously without issues.

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Short Term Tractive Effort

Power needed for short-term tasks like climbing steep grades.

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Back EMF

Voltage created by a DC motor as it turns, opposing the applied voltage.

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Auxiliary Loads

Additional electrical needs beyond the primary train power.

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Adhesion

The grip between train wheels and track.

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Power-Speed Curve

A graph showing how power output varies with speed.

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Balancing Condition

When the train's resistance (drag) matches the torque produced by the motors, resulting in a constant speed.

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Balancing Speed

The maximum speed a train can achieve on a specific gradient and curvature for a given load, where TE and train resistance are equal.

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Train Resistance

Forces that oppose a train's motion. These include friction, air resistance, and resistance due to gradients and curves.

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Specific Resistance

Train resistance measured in kg/ton. It's the force needed to start or move a loco or train per ton of its weight.

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Starting Resistance

The force required to overcome static friction and get a train moving from a standstill.

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TE for Starting a Train

The tractive effort needed to start a train is calculated based on the weights of the load, loco, and train, and their respective starting resistances.

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Notches

Steps or stages on an electric locomotive's controller that adjust the voltage applied to the motors, increasing the torque and thus acceleration.

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Jerk of Acceleration

A sudden increase in torque due to the sudden increase in current when a notch is increased.

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TE-Speed Curve

A graph showing the relationship between tractive effort (TE) and speed.

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Train Resistance-Speed Curve

A graph showing the relationship between train resistance and speed.

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Curve Resistance

The force needed to overcome the centrifugal force acting on a train as it travels along a curved track.

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Running Resistance

The total force opposing a train's motion at a constant speed, including rolling resistance, aerodynamic drag, and grade resistance.

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Axle-Load

The weight carried by each axle of a locomotive.

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Specific Grade Resistance

The force per unit weight needed to overcome the incline of a track.

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Back Voltage

The voltage generated within a motor as it is rotating, which opposes the applied voltage.

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Effective Voltage

The voltage that actually drives the motor after considering back voltage and other factors.

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Degree of Curvature

A measure of how sharp a curve is, expressed in degrees. A higher degree of curvature indicates a sharper curve with a smaller radius.

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Radius of Curvature

The radius of the circle that the curved track segment approximates. A smaller radius corresponds to a sharper curve.

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Gear Ratio (in Locomotives)

The ratio of the number of teeth on the motor's gear to the number of teeth on the axle's gear. It defines the speed and torque relationship between the motor and the axle.

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Field Shunting

A technique used in DC motors to increase the speed beyond the basic balancing speed. It involves weakening the magnetic field in the motor by adding an extra circuit.

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Specific Curve Resistance

The amount of force required to overcome curve resistance, measured per unit weight of the train (usually in kg/ton).

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Effect of Gear Ratio on Tractive Effort

The gear ratio in a locomotive determines the relationship between the motor's speed and the train's speed. It affects the force (tractive effort) available at different speeds.

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Effect of Wheel Diameter on Tractive Effort

As wheels wear down, their diameter decreases, effectively changing the gear ratio. This affects the tractive effort at different speeds.

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What is the difference between starting and running resistance?

Starting resistance is the force required to get a train moving from rest. Running resistance is the force required to keep a train moving at a constant speed.

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How does gradient affect train resistance?

Steeper gradients create higher grade resistance, requiring more TE to maintain speed.

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What is the relationship between TE and train resistance?

When TE is greater than train resistance, the train accelerates. When TE is equal to train resistance, the train maintains a constant speed.

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Why does speed decrease when a train climbs a grade?

Climbing a grade increases the train resistance, requiring higher TE. If the TE doesn't increase, the train slows down to balance the forces.

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Study Notes

Tractive Effort and Train Resistance

  • Force and Acceleration: Applying force to a mass causes acceleration, following Newton's laws of motion. Force equals mass times acceleration.
  • Tractive Effort (TE): The force applied to the train's wheels to cause movement. It's determined by the power equipment and driver control.
  • Energy: Energy used to move an object over a distance is the product of force and distance.
  • Power: Power is the rate of energy usage or energy per unit time. Power equals force times speed or energy divided by time.
  • Power and Speed: Tractive effort varies with speed. At speeds below 20mph, TE is constant, leading to constant acceleration. Above that speed, TE reduces, resulting in decreasing acceleration and a curved speed-time relationship. This is limited by the maximum adhesion between wheels and rails. Maximum Tractive Effort is the maximum TE that can be applied.
  • Maximum Power at Rail: Maximum power at the rail corresponds to the maximum TE (100 kN in example) multiplied by speed = 100kN x (20mph/2.2ms⁻¹)=910 kW
  • Train Resistance: Resistance encountered by the train, increasing with speed. It's calculated as a + bv + cv². Factors include static friction, mechanical factors and air resistance.
  • Types of Tractive Effort: -Starting Tractive Effort: Force needed to start a stationary train without wheel slip. -Continuous Tractive Effort: Force needed to keep a train moving continuously without wheel slip. -Short Term Tractive Effort: Force needed for short durations, such as climbing a grade (up to 120% of continuous TE).
  • Effect of Gradient: Gradients affect train resistance; the greater the incline (gradient), the higher the resistance. Resistance (TG= W/G) where W is train weight and G is the gradient.
  • Effect of Curve: Curves induce resistance (given by Tc=0.4 * S * W)
  • Gear Ratio: Gear ratio affects the minimum and maximum speeds at which the train operates safely.
  • Wheel Diameter: Smaller wheel diameters have higher starting tractive effort but lower high-speed tractive effort.
  • Field Shunt: The current through the field coils of a DC motor is reduced by increasing the resistance, allowing the train to speed up, however, the power decreases.

Additional Points

  • Speed vs. Time curves illustrate how speed changes over time based on acceleration or deceleration.
  • Power vs. Speed graphs display the relationship between power output and train speed.
  • Balancing conditions are the point where tractive effort equals train resistance, allowing for a constant speed.

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