Physics/engineering nerds help me out here (horsepower vs. mass vs. acceleration)

[shovel]

I was thinking about how lightweight cars feel obviously faster with less horsepower - example my mildly spiced up 94 GT leaps away from a stoplight like a surprised cat compared to my hemi powered RCSB ram 1500.

If I generously pretend my Mustang has 240 horsepower that's 60% of the Ram's 395. The weight according to LMR is 3276 pounds plus my 225 = 3501 and the weight of my truck + me is usually between 5000 and 5050 when I leave the dump according to their scale. 3500 is ~70% of 5025, and yet with 60% as much power it feels "twice as fast" subjectively to me.

If I go to this 0-60 calculator which claims it was created by a guy with PhD after his name and reviewed by another guy whose bio says he's a physicist, doubling engine power while doubling weight = identical 0-60 times.


Similarly if I calculate kinetic energy for an object using 1/2mv² an object with 2x the mass has 2x the joules of kinetic energy when traveling at the same velocity.

So it would seem that a car which is twice as heavy and has twice the horsepower should feel the same, but somehow we all still know when we're in a zippy little car with the same power to weight ratio as a heavier car with a bigger engine. It can't all be visual and auditory clues.. can it?

Am I just imagining that my 14.59 pound per horsepower Mustang is faster than my 12.72 pound per horsepower Ram?

 

[dalpoas83]

I read it wrong at first then I had to change my answer. Not an engineer or a physics guy but avid car enthusiast. Lot of things in the equation though other than horsepower. Torque comes to mind, transmission, gearing, suspension, tire grip, aerodynamics, etc. You already know that though

 

[lwarrior1016]

A big thing to remember is torque produced by the engine, and torque multiplication through gear ratios and tire size.

Where an engine makes its power in the rpm band will also affect how it feels.

 

[GTamas]

I imagine gearing and tire size is a huge factor in zippyness.

 

[r3dn3ck]

Well now... time to shine for r3d

The first thing you have to remember is that HP is not a measure of power as most people understand it (I'll come back to this), it's a measure of the rate that work is done. Torque is a measure of how much force is applied in order to do work and this is how the layman will understand the word "power". The layman is prone to misapplying technical terms so I'll steer clear of the technical uses of the terms as much as possible in what follows so all the other science nerds can put down their pitchforks and torches and STFU while I try to explain a very simple thing to a layman without being a picky dick about terminology.

The short version is: Torque is for go, HP is for show.

The second thing to remember is that there's a thing called inertia which has to be defeated for any motion to occur. One component of inertia is mass. Heavy things have a lot of inertia, light things have little inertia.

The third thing to remember is that engines do not produce peak torque at all RPM's, they have to wind up a little bit first but that requires the vehicle's speed to be increased from zero. This is where OP's observation that brutishly strong heavy vehicles don't feel fast off the line comes from. Once the things are moving and they're able to stay in the power band then the pickup with a higher power to weight ratio would out accelerate the Mustang.

Now, coming back to the technical terms "work" and "power", both are basically describing the same thing, the exchange of force over time and what happens as a result. Work requires motion to exist as a non-zero value. Force is how much pressure is being applied but it doesn't require motion to exist as a non-zero value.

To simplify things and step away from technical terms that are nothing but confusing to the layman, think of it this way: My ass produces a constant force on the couch without doing any work so my ass produces a good amount of torque on the end of the couch I sit on whilst sitting on the couch but does no work while sitting on the couch. To elaborate a little further: If you put a breaker bar on a nut (assuming the breaker bar has no mass) and stick a weight on the end of it, you're applying torque to the nut. Without sufficient mass on the end of the bar the nut doesn't turn. If the nut doesn't turn then you're not doing any work, you're generating zero horsepower. It matters that the nut doesn't turn. If you increase the force (torque) applied to the nut sufficiently then the nut will begin to rotate, the more torque force you apply the faster the nut will turn. If you apply a variable amount of force then the rate of rotation will vary accordingly. And now we'll get into the why of OP's observation...

Engines that leverage high RPM are saying, "Look I don't make shite for power but I can still do a lot of work if you wind me up really fast." Engines that make planet turning torque don't need to (and for various reasons usually don't) generate much in the way of RPM. They're saying, "I'm big enough to do the job I was assigned without getting my heart rate up and it's bad to get my heart rate up."

Big heavy things with small engines stress the piss out of those engines. Small light things with big engines stress the piss out of the small things that carry their engines.

Now onto the big one, inertia. Inertia is resistance to motion or more exactly to a change in motion. Your big heavy pickemup truck weighs a lot and the big engine in the big truck makes a lot of power but it doesn't make that power evenly at all rpm, it still has to wind up a bit before it comes onto the cam and starts really putting the smack down. Your observation that the big truck should be faster if the power to weight ratio is better is correct only in a universe where the engines of both vehicles make peak torque at all RPM's, but they don't. Ignore the HP:Weight ratio and look at the torque:weight ratio at WOT at 1200rpm. That should explain everything to you.

In order for your pickup to move off the line like your mustang it would need to generate frame bending torque just off idle. In order for your mustang to ultimately out accelerate the pickup it would need either to operate at a much higher peak rpm than it currnetly does or to have some laggy power adder like too big of a turbo or a nitrous kit that you don't activate until half track.

 

[GTamas]

Interesting thread, thanks for explaining. So with shorter gear and lower weight you are basically reducing the inertia?

 

[shovel]

It's probably not a bad idea to mention that I used two specific RWD, pushrod V8 powered vehicles I currently own as examples because it made sense to compare them.. but like a lot of folks here I'm going grey and have driven & been passenger in many cars over the years and it would be pointless to focus only on those two examples.

I think for most of us if we were blindfolded and sat in the passenger seat of random cars and sent down a drag strip, then asked "was that a light car with a little power or a heavy car with a lot of power" we'd somehow be able to tell with our butts regardless of any specific car's gearing, torque curve, etc. Maybe I'm wrong about that.

Every automotive journalist reviewing cars will make a point of talking about heavy cars being unavoidably heavy, sometimes complimenting the manufacturer on "hiding the weight", which wouldn't be necessary if it wasn't a real thing people feel with their butt-o-meter.

I work within an engineering team but my work is electricity and air so I'm very rusty on mech. professionally. Still I have been a lifelong wrench bender and it was necessary to study this in school - I'm hardly new to the concepts of horsepower and torque and gearing.

The part that has me curious is likely more related to the 1/2mv² bit than the final drive ratio or engine torque curve. An object going twice as fast has four times the kinetic energy which is part of why doubling your horsepower would not double your 1/4 mile trap speed even if all other variables were accounted. But an object twice as heavy going the same speed only has twice the kinetic energy, so an occupant in a car of any weight should experience the same acceleration as long as the power to weight ratio is the same.

We don't have access to nice lab rigor, with identical cars differing only in weight with all other variables tied up. The thing any of us reasonably has is a breadth of experience with our butt dynos.

 

[r3dn3ck]

I imagine gearing and tire size is a huge factor in zippyness.

Small changes in gearing and large changes in tire size do have a strong effect. Small changes in tire size not so much.

It's probably not a bad idea to mention that I used two specific RWD, pushrod V8 powered vehicles I currently own as examples because it made sense to compare them.. but like a lot of folks here I'm going grey and have driven & been passenger in many cars over the years and it would be pointless to focus only on those two examples.

I think for most of us if we were blindfolded and sat in the passenger seat of random cars and sent down a drag strip, then asked "was that a light car with a little power or a heavy car with a lot of power" we'd somehow be able to tell with our butts regardless of any specific car's gearing, torque curve, etc. Maybe I'm wrong about that.

Every automotive journalist reviewing cars will make a point of talking about heavy cars being unavoidably heavy, sometimes complimenting the manufacturer on "hiding the weight", which wouldn't be necessary if it wasn't a real thing people feel with their butt-o-meter.

I work within an engineering team but my work is electricity and air so I'm very rusty on mech. professionally. Still I have been a lifelong wrench bender and it was necessary to study this in school - I'm hardly new to the concepts of horsepower and torque and gearing.

The part that has me curious is likely more related to the 1/2mv² bit than the final drive ratio or engine torque curve. An object going twice as fast has four times the kinetic energy which is part of why doubling your horsepower would not double your 1/4 mile trap speed even if all other variables were accounted. But an object twice as heavy going the same speed only has twice the kinetic energy, so an occupant in a car of any weight should experience the same acceleration as long as the power to weight ratio is the same.

We don't have access to nice lab rigor, with identical cars differing only in weight with all other variables tied up. The thing any of us reasonably has is a breadth of experience with our butt dynos.

Butt dyno would experience zero difference if the torque at the wheel to weight ratio is identical at all tire speeds. No lab needed, physics doesn’t care about rigorous testing protocols. If the maths say it will be so, it will be so.

Gearing ratio changes to a numerically larger gear is not reducing inertia as a technical matter, but it can be thought of in that way. The inertia of a body at rest in a static system does not change. Increased mechanical advantage with a bigger gear is not different to using a longer lever to turn a bolt. This is why gearing changes have such a strong effect. Massive decreases in tire diameter work in the exact same way but gears in final drive units are much easier to make large changes to. Going from a 3:1 to a 4:1 gear can be done more practically than going from a 28 inch tall tire to a 21 inch tall tire. The effect is similar though.

 

[duh09]

One thing to consider on these vehicles, it all comes down to tuning and the transmission and how its actually putting that power down. 395hp looks good on a sales brochure but that Ram isn't making 395hp from 0-6000rpm, it's touching it at one point in time and that's it, so comparing a peak number to a peak number means very little across the range in the grand scheme of things and a lot of modern higher hp vehicles are tuned in such a way that it doesn't even allow it to put full power down in the first couple of gears to save the trans.

Feel is also super subjective and has a million different things playing into how "fast" something feels. Modern minivans are going to outrun our SN95s once up to speed, but the soccer mom isn't scared because it isn't swinging the ass end and laying rubber down in that process.

The reason I love SN95 cars is because they're shitty enough to feel rowdy, even without a lot of power. Getting one to step out and slide around and burn tires is super easy to do, even with not a lot of power getting down to the wheels. My Corvette that I had made 700whp and it all stuck, so besides the initial hit of putting you back in the seat, it just hooked and went and honestly it got pretty boring. My raggedy black car might be lucky to put 175hp down on a dyno and is hurting above 5000rpm, but you can slide it around and melt tires from every stop light so it "feels" fast even if my Powerstroke would outrun it.

Physics matter a lot in it, but there's not a great way to factor in every variable to nail down exact hp/tq to speed and feel unless you have an identical car and ramp power up through tuning to different power levels to compare.

 

[joemomma]

One other thing to consider, maths aside, is that in the SN95 you're essentially sitting on the ground (one reason my wife doesn't like riding in it). It's a totally different sensation than sitting up in a truck or the SUV that she is used to.

My dad and I had a similar conversation a few months ago. He's got a '19 F-150 3.5EB, I think they're rated at like 375HP. His complaint was that it didn't "feel" fast or "feel" like 375HP. He grew up in the muscle car era, and always compares things to those cars. I always have to remind him that his truck weighs twice what one of those cars did.

 

[Musturd]

One other thing to consider, maths aside, is that in the SN95 you're essentially sitting on the ground (one reason my wife doesn't like riding in it). It's a totally different sensation than sitting up in a truck or the SUV that she is used to.

My dad and I had a similar conversation a few months ago. He's got a '19 F-150 3.5EB, I think they're rated at like 375HP. His complaint was that it didn't "feel" fast or "feel" like 375HP. He grew up in the muscle car era, and always compares things to those cars. I always have to remind him that his truck weighs twice what one of those cars did.

Meanwhile the eco boost is faster than a lot of the coolest muscle cars from the 70’s . Just not nearly as cool .

 

[shovel]

in the SN95 you're essentially sitting on the ground

That is the opposite of what I usually hear from people.

 

[Musturd]

That is the opposite of what I usually hear from people.
View attachment 35246

I feel you . Corvettes and 70’s trans ams you’re literally on the floor

 

[ttocs]

I had a buddy in high school that picked up an old MG for a short time. I remember the two of us cramming inside of it and then when we were going down the highway I looked over at a semi trailer to see its rear wheel odometer was just about at eye level in the middle of the wheel.

 

[95opal]

One thing to consider on these vehicles, it all comes down to tuning and the transmission and how its actually putting that power down. 395hp looks good on a sales brochure but that Ram isn't making 395hp from 0-6000rpm, it's touching it at one point in time and that's it, so comparing a peak number to a peak number means very little across the range in the grand scheme of things and a lot of modern higher hp vehicles are tuned in such a way that it doesn't even allow it to put full power down in the first couple of gears to save the trans.

Feel is also super subjective and has a million different things playing into how "fast" something feels. Modern minivans are going to outrun our SN95s once up to speed, but the soccer mom isn't scared because it isn't swinging the ass end and laying rubber down in that process.

The reason I love SN95 cars is because they're shitty enough to feel rowdy, even without a lot of power. Getting one to step out and slide around and burn tires is super easy to do, even with not a lot of power getting down to the wheels. My Corvette that I had made 700whp and it all stuck, so besides the initial hit of putting you back in the seat, it just hooked and went and honestly it got pretty boring. My raggedy black car might be lucky to put 175hp down on a dyno and is hurting above 5000rpm, but you can slide it around and melt tires from every stop light so it "feels" fast even if my Powerstroke would outrun it.

Physics matter a lot in it, but there's not a great way to factor in every variable to nail down exact hp/tq to speed and feel unless you have an identical car and ramp power up through tuning to different power levels to compare.

100% with this /\/\
Peak numbers are for dyno queens. The highest average number under the curve is where its at. This is why cams matter.

 

[shovel]

that Ram isn't making 395hp from 0-6000rpm,

It's probably not a bad idea to mention that I used two specific RWD, pushrod V8 powered vehicles I currently own as examples because it made sense to compare them.. but like a lot of folks here I'm going grey and have driven & been passenger in many cars over the years and it would be pointless to focus only on those two examples.

I think it's probably fair to say that the 2015 Hemi with variable cam timing and variable intake geometry has a much flatter torque curve than a 1994 SBF equipped with neither of those technologies.

Anyway I guess the conclusion is probably going to be that if acceleration is the only metric, as long as power and weight scale with each other (all else equal) the feeling of acceleration by occupants will be the same so if our butts are telling us something different that's other clues we're interpreting like engine noise or suspension input or just what our eyes are trying to tell us.

 

[joemomma]

There's certainly a big role played by our senses and how we perceive things. Some cars just "seem" faster than others. A prime example is my wife's RX350 SUV. While it isn't fast by any means (although likely faster than my SN lol), if you aren't really paying attention you'll find yourself running 85-90 without even meaning to. Another example I like to use is the CTS-V coupe (6-sp) my nephew had. It had been worked (pulley/tune, full suspension, etc.), I think it was 540 to the tires or so. It was without a doubt one of the fastest street cars I've ever been in. When he took of, it just went yonder at a great rate of speed. No tire squeal, no sideways, nothing, just straight-line acceleration. You just knew you were going fast.

 

[duh09]

I think it's probably fair to say that the 2015 Hemi with variable cam timing and variable intake geometry has a much flatter torque curve than a 1994 SBF equipped with neither of those technologies.

Anyway I guess the conclusion is probably going to be that if acceleration is the only metric, as long as power and weight scale with each other (all else equal) the feeling of acceleration by occupants will be the same so if our butts are telling us something different that's other clues we're interpreting like engine noise or suspension input or just what our eyes are trying to tell us.

Sure it might have a flatter curve, but you're ignoring the rest of that statement and what really matters there - it likely is not putting down all of its power in the first couple of gears. All of that technology is why you're not getting a huge burst of power and taking off like a rocket from a stoplight - because the ECU is likely limiting power right out of the hole to protect the trans and your traction control nannies are keeping your tires from breaking lose too much - a 94 Mustang has none of that. From a jump, it'll do whatever you're inputting. The Ram probably has flatter torque curve and more power but the point I'm getting at is that it is not getting put down 24/7.

My ole 05 SRT4 back in the day is a pretty stripped down low tech car, it had nothing for traction control, but the ECU wouldn't allow it to build full boost until 3rd gear to give it some chance of hooking and to not grenade the trans immediately. Ford in 1994, with their ECU based on 1986 technology sure what not putting anything like that into play.

 

[shovel]

I regret bringing up any specific vehicles because that seems to really be a hangup here.

Anyway I don't think anything more can come from this, have a good day fellas.

 

[duh09]

I regret bringing up any specific vehicles because that seems to really be a hangup here.

Anyway I don't think anything more can come from this, have a good day fellas.

There's no hang up.

Less weight = faster.
More power = faster.
Less weight and more power = more faster.

It doesn't take complicated physics and engineering to figure that out because it's that simple equation you posted to calculate energy and all that.

The problem is there is no way to talk about how fast something "feels" when comparing a 4000lb vehicle with 400hp and a 2000lb vehicle with 200hp because there's a million different variables that are going to play into real world acceleration with real world cars with real world 4000lb/400hp and 2000lb/200hp.

If the cars have the same wind resistance and center of gravity and suspension and whatever and you can magically adjust on a scale from 1000lb/100hp to 5000lb/500hp and give them the same grip and same torque curves and same trans tuning and same everything, and only adjust weight/power and keep the ratio, it'll accelerate the exact same and feel the same.

But there's no way to do that, so we are going to compare real world vehicles and talk about why they feel different.

You seem to be the one that gets hung up on theoretical silliness without considering that fact that we exist in a real world with real things that we can talk about and measure. If you want to create some word problems for a physics textbook, you're on your way.