What is the relationship between acceleration and fuel economy?
 

I'm taking calculus I. How do I relate this question to calculus? I have a vague idea of what the relationship is but not regarding calculus if there is one.
Thank you for your help.

I would have to think for quite awhile to figure an answer, but maybe this will help. Acceleration is the anti-derivative of torque and BSFC charts might help relate it to fuel consumption.

Good Luck, Matt

Brake Specific Fuel Consumption (BSFC) Maps - EcoModder

Start by looking at two cases:

Case 1: Assume a constant low acceleration to a speed. You reach that speed at a distance. Use the engine BSFC chart, gear ratios, and rear axle ratio to find fuel used.

Case 2: Assume a constant high acceleration to the same speed, then constant speed to the same distance as Case 1. Use the engine BSFC chart, gear ratios, and rear axle ratio to find fuel used.

Note that the engine efficiency (BSFC) varies with RPM and throttle opening. The variable engine efficiency is outside the scope of calculus I, so this problem cannot be solved using calculus I math. It would be a good problem for a class in numerical analysis, though.

And good luck with your calculus class. Calculus II and III are even more fun!

Calculus is one of the few classes I attempted at the community college (I took the rest with hundreds of my closest friends at the university) and I still could not manage it, so I was deprived of the additional fun of subsequent mathematics courses.

Good luck learning a little bit more about how the universe works.

The relationship between acceleration and fuel economy COULD look like a flattened bell curve, with very similar fuel economy through light-medium acceleration but worse economy at high acceleration and very low acceleration.

I hated calc 1, took me 3 tries to pass.

So I made this:
Attachment 22667

Which I proceeded to ventilate with an assortment of 7.62x54Rs, 9x19s, and 45 ACPs.

I keep the remains in my room, I want to hang it on the wall, but I haven't gotten around to it. I'll post a picture when I get back home.

Edit: Here it is.

Attachment 22670

Isaac Newton
 

:D:
About 20 years ago at work, I was visiting an engineer's office to chat with him about something.
He had a picture of "sir Isaac" on the wall above his desk. I pointed to the picture and asked him, "Isn't he the @$$h0le who invented calculus?"
We both had a good laugh over that.
The only dealing I've had with calculus since I earned my engineering degree has been getting it scraped off my teeth.:D

Back on topic...
Accelerating on a freeway on-ramp with my Mustang in 3rd gear (with the accelerator pedal about 1/2" from the floor to avoid open-loop-full-throttle enrichment), I get about 8 MPG instantaneous.
I shift @ 2500 RPM.
In 4th gear under the same conditions, I get around 10 MPG.
In 5th gear under the same conditions, I get around 15 MPG.
My average over the past 3 years is over 32 MPG.
How you accelerate doesn't affect your average fuel economy nearly as much as how you drive after you accelerate.

I never got to take Calculus in school (maybe I didn't miss much). I don't know for sure if this will help, but I'm thinking an EV calculator like this one may help. EV Calculator

Electricity is still a fuel but electric motors don't have as many variables, (pumping losses etc.) Torque curve is flatter. Hope it helps.

1/2 off topic, I was playing around with some hyperloop acceleration/deceleration/time at speed math and how long it would take to get different distances. Then I came across a post talking interstellar travel, constant acceleration, and relativity and my mind was blown again. I can never get enough trying to comprehend those kinds of speed and distances.

I suspect the hardest part will probably converting the BSFC for a given engine into a purely mathematical formula that has a high enough correlation to the real BSFC of that engine .. Calculus needs the pure math formula to work with first .. You can't do calculus on the picture/graph 1st , you have to convert it to pure math 1st.

The rest is just combining all the relevant formulas .. and imputing all the variable data for a given engine , vehicle , environmental conditions ,etc.

At it's core .. acceleration is just the rate (power) at which some source of input energy (fuel) is being converted into kinetic energy of motion (minus all the sources of drag (Aero, Rolling, Gravity, etc) that are bleeding applied power/energy away).

The BSFC for given conditions tells you what the conversion efficiency is .. for fuel to shaft .. for any given rate of torque/force/RPM/Power/Energy .. that you need to achieve some desired rate of acceleration.

I was awright at calculus, no genius but able to keep up.

Promptly forgot all that was taught afterwards.