# Dynamics assignment, power output of car

• JamesB93
In summary: The problem statement says to use the pressure drop at the inlet, which is 55% of atmospheric pressure.
JamesB93
I'm currently studying Mechanical Engineering at Level 3 in the UK and I'm beginning my integrated masters in September. I've missed a large chunk of my studies this year due to a broken collarbone I sustained earlier in the year. Instead of getting any special dispensation I'm trying to work my way through my assignments now despite having very little lesson time.
I'm working through my Mechanical Principles: Dynamics assignment now and I've hit a wall on a question and just can't figure out how to advance.

The question word for word is:
Part 1:

A Manual 5-speed Vauxhall Corsa 1.4 16v with an all-up mass of 1,260kg is used to drive up a hill with an incline of 10% at 65km/hour.

If the driver applies the brakes as if undertaking an emergency stop and slows the car down to 30km/hour in 2.5 seconds, calculate the distance traveled under braking and the energy dissipated in each of the 4 brakes if the front:rear braking effort is split 60:40. Ignore all friction and aerodynamic losses.

If the driver now coasts up the hill until the car comes to a rest, calculate, ignoring losses due to friction and aerodynamics, the additional distance traveled and the potential energy increase whilst coasting.

Part 2:
The engine has a bore of 77.6mm and a stroke of 73.4mm. If the volumetric efficiency is 44% and the pressure drop at the inlet is 55% of atmospheric pressure at an engine speed of 6,000rpm, calculate the power output at the flywheel when the calorific value of the fuel is 47,850kJ/kg.K. Take atmospheric pressure as 1.01 bar, ambient temperature as 20C and the mass air/fuel ratio as 14.7:1/

If the car is driven at an engine speed of 6,000rpm in 3rd gear with a gear ratio of 1.41:1 with a final drive gear ratio of 3.94:1. calculate the driveline torques at the output of the gearbox if the efficiency of the gearbox is 97% and the final drive efficiency is 89%.

Now I think I'm fine on part 1, I seemed to do all the calculations there with relative ease, but on part 2 I've completely hit a brick wall, if someone could take me through the correct method of calculating the answers without giving me the answers I'd greatly appreciate it. My first attempt at calculating this indicated that this 1.4 litre Vauxhall was outputting 6,350bhp and using 168 litres of fuel a second so I know I'm going insanely wrong somewhere.

This is my first forum post so if I've misplaced my post or broken any rules please let me know (but don't tell me off :().

I seem to have had a clarifying moment, I was taking the air:fuel ratio for volume, not mass.
I did ((pi*bore2)/4)*stroke to get the swept volume of each cylinder. I then multiplied that by 4 to get the total swept volume of the engine and divided it by 2 because the pistons only intake air on every other engine revolution. I then multiplied this by the engine's volumetric efficiency to get the actual air intake per revolution. I then multiplied this by the revs per minute and divided it by 60 to get the air intake per second. I looked online and found a mass/m3 value of 1.2kg/m3 for air at 1.01bar and 20C. I multiplied the air intake per second by 1.2 to get the mass of air per second, then divided it by 14.7 to get the intake of fuel in kg/second. I multiplied this by the calorific value of the fuel and multiplied it by 1000 to get the power output of the car in watts and converted that to bhp by dividing it by 745.7 to give me a power output of approx 160bhp.
I'm a little worried that I didn't use the value of 55% pressure drop at the inlet and and didn't account for the value for what I assume is temperature in the calorific value of the fuel.

JamesB93 said:
I multiplied this by the calorific value of the fuel and multiplied it by 1000 to get the power output of the car in watts and converted that to bhp by dividing it by 745.7 to give me a power output of approx 160bhp.

160 bhp is a pretty robust output for an engine of this size without a turbocharger.

Checking rated output figures online for this model engine shows an output of about 90-100 bhp. It's not clear what the exact model engine is being used in this car, but these output figures seem to be fairly constant for several different models. The outputs are quoted at slightly lower RPMs than 6000 as specified by the problem statement.

http://en.wikipedia.org/wiki/GM_Family_1_engine

I'm a little worried that I didn't use the value of 55% pressure drop at the inlet and and didn't account for the value for what I assume is temperature in the calorific value of the fuel.

There seems to be a mistake in the units of the calorific value of the fuel. The correct units should be kJ / kg.

Given the comments above, this is perhaps a reason that the pressure drop at the engine air intake should be taken into account.

Those are my (very) rough notes on the engine power output so far. Apologies for the handwriting, combination of dyslexia and recovering collarbone.
As I said previously, the calorific value of the fuel is in kJ/kg.K and I haven't accounted for the K on the end of that and I haven't accounted for the "pressure drop at the inlet of 55% of atmospheric pressure". Which both worry me. Can anyone see where I'd factor those in without getting a number for horsepower that's in the thousands.

JamesB93 said:

Those are my (very) rough notes on the engine power output so far. Apologies for the handwriting, combination of dyslexia and recovering collarbone.
As I said previously, the calorific value of the fuel is in kJ/kg.K and I haven't accounted for the K on the end of that and I haven't accounted for the "pressure drop at the inlet of 55% of atmospheric pressure". Which both worry me. Can anyone see where I'd factor those in without getting a number for horsepower that's in the thousands.

As I said in my previous post, the problem statement seems to be using incorrect units for the calorific value of the fuel. The correct units should be kJ / kg (No K).

SteamKing said:
160 bhp is a pretty robust output for an engine of this size without a turbocharger.

Checking rated output figures online for this model engine shows an output of about 90-100 bhp. It's not clear what the exact model engine is being used in this car, but these output figures seem to be fairly constant for several different models. The outputs are quoted at slightly lower RPMs than 6000 as specified by the problem statement.

http://en.wikipedia.org/wiki/GM_Family_1_engine
There seems to be a mistake in the units of the calorific value of the fuel. The correct units should be kJ / kg.

Given the comments above, this is perhaps a reason that the pressure drop at the engine air intake should be taken into account.

Okay if I account for the pressure drop and use it to alter the mass of the air as it enters the engine, then follow on with those numbers I get 71.98 horsepower.
Checking online I can see that the maximum output of one the 1.4 litre Vauxhall Corsa 5 speed manuals are in the range 85-100. I'll query with my lecturer on the units for calorific value, maybe he's gotten confused with specific heat capacity there.
Do you think 71.98bhp seems a reasonable answer to this?

Thanks for all the help, you're a life saver.

JamesB93 said:
Do you think 71.98bhp seems a reasonable answer to this?

It seems like a reasonable figure.

## 1. What is the definition of "dynamics" in relation to a car?

Dynamics refers to the study of how objects move and interact with forces. In the case of a car, it involves understanding how the car's motion is affected by various forces such as gravity, friction, and engine power.

## 2. How is the power output of a car measured?

The power output of a car is typically measured in units of horsepower (hp) or kilowatts (kW). This measurement is determined by using a dynamometer, which measures the torque and rotational speed of the car's engine.

## 3. What factors affect the power output of a car?

The power output of a car is affected by various factors such as the size and design of the engine, the quality of fuel, and the efficiency of the car's transmission system. Other factors that can impact power output include temperature, altitude, and air resistance.

## 4. How does power output affect a car's performance?

The power output of a car directly affects its performance, specifically its acceleration and top speed. A higher power output means the car can accelerate faster and reach higher speeds. However, other factors such as weight and aerodynamics also play a role in a car's overall performance.

## 5. Can the power output of a car be increased?

Yes, the power output of a car can be increased through modifications such as adding a turbocharger or supercharger, upgrading the engine components, or tuning the engine's computer system. However, it is important to note that increasing power output may also affect the car's reliability and fuel efficiency.

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