FORMULAS.

 

i Personally like using big dc electric motors hooked up to the engine by a gear reduction drive with the motor/generator attached to a variable load with a really good multimeter in the middle so basically the more watts the more hp (they can be converted) and the only guessing is the pourcentage of hp lost in the system

 

i Personally like using big dc electric motors hooked up to the engine by a gear reduction drive with the motor/generator attached to a variable load with a really good multimeter in the middle so basically the more watts the more hp (they can be converted) and the only guessing is the pourcentage of hp lost in the system

I have looked at using a Gen Head. Most of these Old Sled Single Cylinder Motors were in the 12hp to 36hp Stock. In Racing form maybe up to 65hp if turning high rpm. Ultralight Engines use Max 6500rpm. So the 277UL, 377UL, 447UL, 503UL, are Max 50hp with a Muffler, but can be up to 70hp with a Good Tuned Pipe.

A CHICAGO ELECTRIC

10,000 Max Starting / 7200 Running Watts Generator Head. At 3600rpm!
$479.99

The whole Fluid Dyno was $500 for Small Cart Engines. I'm mainly interested in the 25hp to 40hp Engine range for now.

How much are these DC Motors your talking about? How would you write the Formula DC to hp?

The 250 Type 247 Single was 12hp@5500rpm. A 10,000w Generator Head = 13.4hp. 5500rpm/3600rpm = 1.527 Ratio. 6500rpm/3600rpm = 1.805 Ratio. That 10,000w Size Gen Head wouldn't allow you to do to many Mods to that Engine. 248cc/7cc= 35.4hp. A Polini Thor 250 DS is rated 36hp@7200rpm.

 

The whole Fluid Dyno was $500 for Small Cart Engines. I'm mainly interested in the 25hp to 40hp Engine range for now.
.

Have you priced the larger pump you will need? One in the video only good for about 10hp

50hp = 50 gpm @1500 psi at 100% efficiency.

Northern has one in the ball park- 48GPM.

$518

 

Have you priced the larger pump you will need? One in the video only good for about 10hp

50hp = 50 gpm @1500 psi at 100% efficiency.

Northern has one in the ball park- 48GPM.

$518

I'm still doing research, but If I understand it right, you can use different Belt/Gear Ratios. At 1:1, Yes the Hyd Pump is good up to X amount of Hp. Like this $120 Hyd Pump on eBay has a 12gpm, 3200psi, at 3000rpm rating.

Which at 1:1 Ratio is good for 22.4 hp. You input the correct ratio used in the Software.

At 1:1 at 12gpm, 3200psi, 3000rpm = 22.4hp

At 2.0 at 12gpm, 3200psi, 3000rpm = 44.8hp

At 3.0 at 12gpm, 3200psi, 3000rpm = 67.2hp

For these Old Sled Engines and Ultralight Engines were looking at 12hp to 65hp and using 5500rpm to say 7500rpm.

For Sleds/Ultralight Engines I think this Hyd Dyno could be simplified. Finding the right Pulley to Work with the Clutch to make up your Ratio to work would be the hardest.

Here is another Type of Small Brake Dyno that looks interesting and Cheap to build also.

 

HP = Pressure(psi) x GPM / 1714

HP = Torque ft lbs x rpm / 5252

 

I'm still doing research, but If I understand it right, you can use different Belt/Gear Ratios. At 1:1, Yes the Hyd Pump is good up to X amount of Hp. Like this $120 Hyd Pump on eBay has a 12gpm, 3200psi, at 3000rpm rating.
Which at 1:1 Ratio is good for 22.4 hp. You input the correct ratio used in the Software.

At 1:1 at 12gpm, 3200psi, 3000rpm = 22.4hp
At 2.0 at 12gpm, 3200psi, 3000rpm = 44.8hp
At 3.0 at 12gpm, 3200psi, 3000rpm = 67.2hp

Don't think it works that way - could be wrong

The Horsepower formula in the chart is
Hp = GPM x Pressure /1714
67.2 hp x 1714 / 3200lbs = 36 GPM.

The gearing RPM conversion in the video was to determine the GPM flow at various rpms.
His pump was rated at 1.52 cubic inch per revolution. So he needed the gearing to figure Engine RPM vs Pump rpm to get GPM.

At common engine 3600rpm - his pump is putting out
(3600rpm x .278) x 1.52ci /231 = 6.6gpm
To figure HP at 3600 rpm Multiply 6.6 GPM and pressure from gauge.

Going to get tricky doing a full rpm dyno sweep - maybe that is where software is coming from.
If engine rpm is 3600 the pump is making 6.6 GPM
Then at say 2500 rpm the pump is making 4.6 GPM
And at 4200 rpm the pump is making 7.7 GPM

So at every engine rpm you want to look at - you need to change the calculation
HP= (GPM@RPM) x PSI / 1714

I think there is also a long conversation on why you don't want to choose a pump based on full rated RPM, full rated GPM and full rated PSI. Comes from how Dyno tests are normally done.

Plus if you look at the ratings of the hoses in the parts list - 2250psi max.

 

Cheap simple solution
Used gen head connected to engine no crazy formulas no math no testing just hook the motor up and mesure the output in watts
Or you could struggle with a hydraulic system designed for a smaller engine
Even if the hydraulic system worked perfect your results would be inaccurate because of the drag of all the fluid and parts involved

 

3D Model of Small Engine Brake Dyno.

.

SFL-01 Motor Dynomometer V2.0

https://grabcad.com/library/sfl-01-motor-dynomometer-v2-0-2

 

Don't think it works that way - could be wrong

The Horsepower formula in the chart is
Hp = GPM x Pressure /1714
67.2 hp x 1714 / 3200lbs = 36 GPM.

The gearing RPM conversion in the video was to determine the GPM flow at various rpms.
His pump was rated at 1.52 cubic inch per revolution. So he needed the gearing to figure Engine RPM vs Pump rpm to get GPM.

At common engine 3600rpm - his pump is putting out
(3600rpm x .278) x 1.52ci /231 = 6.6gpm
To figure HP at 3600 rpm Multiply 6.6 GPM and pressure from gauge.

Going to get tricky doing a full rpm dyno sweep - maybe that is where software is coming from.
If engine rpm is 3600 the pump is making 6.6 GPM
Then at say 2500 rpm the pump is making 4.6 GPM
And at 4200 rpm the pump is making 7.7 GPM

So at every engine rpm you want to look at - you need to change the calculation
HP= (GPM@RPM) x PSI / 1714

I think there is also a long conversation on why you don't want to choose a pump based on full rated RPM, full rated GPM and full rated PSI. Comes from how Dyno tests are normally done.

Plus if you look at the ratings of the hoses in the parts list - 2250psi max.

Still researching this like I said. The guy that showed the Formula using a Reduction which his was using 10/36 = 0.2777 rounded up to 0.278 Ratio. The Hyd Pump I showed is Bigger Volume than what he used and that RPM and PSI I gave is normal running condition, it will make more. You also can Factor in hp loss. Hp made at the PTO vs hp to the Track or Wheels.

None of this Dyno's or Formulas is going to be100% Exact down to 4 Decimal Places! There is always a +/- X Amount f hp! But it's the Best we have. You know some of the Factory Rated hp for these Engines. Like a 250 Type 247 was rated 12hp@5500rpm. You know they usually Round up hp Numbers so not 100% Correct! But you also have similar Designed Engines to maybe get an Avg hp made for CC used. The 250 Type 247, the 299/300, 318/320, 335 were all built and rated at same rpm, just different Bores & Strokes. So if you put a 250 Type 247 on your Dyno and it makes 11.6hp@5500rpm you know your in the Ball Park! You might even have multiple same Engines to Test to get an Average between 3-5 Engines. Like I got 3-4 335's, but only (1) 250 Type 247.

It would be nice to make the Dyno portable, maybe go to a Swap Meet and maybe Dyno some different Small Engines to get Data.

Taking a 250 Type 247 Single through the different Stages of possible Modifications to make more hp, would be awesome! A Polini Thor 250 is rated 36hp@8000rpm using a 28mm Carb, 11.5cr, with a Tuned Pipe. The 246 Blizzard I have seen rated at 24hp and 29hp rating for it, but not what rpm they used or CR used. Every Engine, Cylinder, has only some hp it can make for a Hot Trail Sled or Racing, Can you maybe Machine some of these Parts to go a little bigger, Yes.

Using better Instruments to measure your Data Collected will Help make your results more Accurate. Like he used a Hyd Pressure Gauge that deals in Whole numbers. Is their a Digital Hyd Pressure Gauge that would give a more Accurate Reading to (4) Decimal places? He was trying to keep Cost down to around $500. You could probably make it for less if you walked a few Scrap Yards for Materials. it all depends on How Inventive you are.

If the Hyd Pump can be used with Reduction Gearing and using MATH to figure out HP, a Gen Head probably could be used the same Way also. HF Sells a 10,000 watt Gen Head for $480 alone. I do have a Military rated 10kw at 10,000 ft Generator on a Skid, weighs about a 1000 lbs. I was told at my 940' it would probably make about 15kw. It has a Small 084 Continetal 4 Cylinder Engine, I call it a Mini 0-200. They have been used successfully on Planes making 45hp.

 

My 10kw Military Gen Looks Like this one on eBay only Army Green.

 

Continental 084 Engine 45hp stripped down for Airplane use.

 

Cheap simple solution
Used gen head connected to engine no crazy formulas no math no testing just hook the motor up and mesure the output in watts
Or you could struggle with a hydraulic system designed for a smaller engine
Even if the hydraulic system worked perfect your results would be inaccurate because of the drag of all the fluid and parts involved

Both HYD Pump and Gen Head and Brake Dyno Setups have different obstacles to over come. Use can lose hp through Chain or Belt Drives. Once you have it setup and the Correct Math Numbers entered into the Software it's pretty much Plug & Play. The Bigger the CC Engine you want to Test, some stuff will probably need upgraded. My needs are for 12hp to 65hp Engines, Max 7500rpm for a Sled Engine, Max 6500rpm for an Ultralight Engine.

The whole Concept is to make it for around $500, maybe less if your a good Junk Yard Dog and can do your own Welding and Fabricating, etc. Like I Paid $25 for that 10kw Military Generator years ago to backup my other Generator. Never had to use it, and today, if I find myself the Acreage I want, I'll probably just use (2) New Generac's hook up to LP in the Country, One for the House and one for the Shop, but set them up to Backup the other. You lose Power they turn on almost instantly, so Work even when your gone.

I could sell the 084 Motor and maybe use the Gen Head to do the KW to HP route. I still Researching and need to figure out how they figure the HP/TORQUE using the Reduction Drive for bigger Engines. The HF Gen Head is Lighter and Smaller and available to everyone. Hyd Pumps have a limit on rpm they can be turned and so do Gen Heads.

At 1:1 Ratio Kw to hp. My Ulralight Engine Spread Sheet for 6500rpm.

 

DATA LOGGERS / COMPUTERS can deal in Tenths of a kw or Hp, and Log Data in 25, 50, 75, 100, 250, 500rpm Increments which ever you setup the Software for. Most People just want to know MAX HP at their desired MAX rpm. Like a setup for the 250 Type 247 might look like this. The Engine is (69mm x 66mm) 246.8cc and 246.8cc/7cc = 35.2hp for 6500rpm, and using the Peak Flow Calc at 94% VE = 35.5hp for 6500rpm.

The Stock 250 Type 247 Cylinder can only handle I believe either a 34mm or 36mm Carb Max without Machining, and even then it can't go much bigger.

A 36mm = 86.5cfm. Flows enough AIR/FUEL for:

86.5cfm/1.5 = 57.6hp

86.5cfm/1.6 = 54.0hp

86.5cfm/1.7 = 50.3hp

86.5cfm/1.8 = 48.0hp

86.5cfm/1.9 = 45.5hp

86.5cfm/2.0 = 43.3hp

A 34mm = 77.1cfm Flows enough AIR/FUEL for:

77.1cfm/1.5 = 51.4hp

77.1cfm/1.6 = 48.2hp

77.1cfm/1.7 = 45.4hp

77.1cfm/1.8 = 42.8hp

77.1cfm/1.9 = 40.6hp

77.1cfm/2.0 = 38.5hp

247cc at 115% VE at 6500rpm = 65 cfm

247cc at 110% VE at 6500rpm = 62 cfm

247cc at 105% VE at 6500rpm = 60 cfm

247cc at 100% VE at 6500rpm = 57 cfm = 38hp per the Peak Flow/Hp Calc. 57cfm/1.6= 35.6hp, 57cfm/1.7= 33.5hp, 57cfm/1.8= 31.6hp, 57cfm/1.9= 30hp!

247cc at 99% VE at 6500rpm = 56 cfm

247cc at 98% VE at 6500rpm = 56 cfm

247cc at 97% VE at 6500rpm = 55 cfm

247cc at 96% VE at 6500rpm = 54 cfm

247cc at 95% VE at 6500rpm = 54 cfm = 36hp per the Peak Flow/Hp Calc. 54cfm/1.6= 33.7hp, 54cfm/1.7= 31.8hp, 54cfm/1.8= 30.0hp, 54cfm/1.9= 28.4hp!

247cc at 94% VE at 6500rpm = 53 cfm

247cc at 93% VE at 6500rpm = 53 cfm

247cc at 50% VE at 5500rpm = 24cfm and says 16hp, so the 12hp rating is lower than 50% VE or the 1.5 Constant is Higher. Notice at 50% VE = 24cfm at 5500rpm vs 100% VE at 5500rpm = 48cfm, double the CFM made for Air/Fuel, so 12hp + 12hp = 24hp@5500rpm! Power Band say 3000rpm to 5500rpm. 5500-3000= 2500/250= 10. Stock 12hp/10= 1.2hp per +250rpm. 24hp/10= 2.4hp per +250rpm. So at 6500rpm is +1000rpm/250rpm= 4 x 2.4hp = 9.6hp + 24hp= 33.6hp@6500rpm at 100% VE. Calc says 38hp, at 95% VE says 36hp, at 90% VE says 34hp.

24cfm/1.5= 16.0hp

24cfm/1.6= 15.0hp

24cfm/1.7= 14.1hp

24cfm/1.8= 13.3hp

24cfm/1.9= 12.6hp

24cfm/2.0= 12.0hp

250 Type 247 Hp Range.

 

Don't think it works that way - could be wrong

The Horsepower formula in the chart is
Hp = GPM x Pressure /1714
67.2 hp x 1714 / 3200lbs = 36 GPM.

The gearing RPM conversion in the video was to determine the GPM flow at various rpms.
His pump was rated at 1.52 cubic inch per revolution. So he needed the gearing to figure Engine RPM vs Pump rpm to get GPM.

At common engine 3600rpm - his pump is putting out
(3600rpm x .278) x 1.52ci /231 = 6.6gpm
To figure HP at 3600 rpm Multiply 6.6 GPM and pressure from gauge.

Going to get tricky doing a full rpm dyno sweep - maybe that is where software is coming from.
If engine rpm is 3600 the pump is making 6.6 GPM
Then at say 2500 rpm the pump is making 4.6 GPM
And at 4200 rpm the pump is making 7.7 GPM

So at every engine rpm you want to look at - you need to change the calculation
HP= (GPM@RPM) x PSI / 1714

I think there is also a long conversation on why you don't want to choose a pump based on full rated RPM, full rated GPM and full rated PSI. Comes from how Dyno tests are normally done.

Plus if you look at the ratings of the hoses in the parts list - 2250psi max.

For Direct Drive you are Correct, but for a Reduction Drive you have to factor that in that Ratio. Hence, he shows 10 Tooth Front and 36 Tooth Rear = .278 Ratio!

 

For Direct Drive you are Correct, but for a Reduction Drive you have to factor that in that Ratio. Hence, he shows 10 Tooth Front and 36 Tooth Rear = .278 Ratio!

Gear reduction has nothing to do with HP. It has to do with pump flow.

Look at the equation where I had it outlined in RED. - He is figuring gallons based on ENGINE rpm not PUMP rpm - Thats why the .258 reduction factor is there.
The overall HP equation does not change.

Very simple math every engine guy should already know shows gear reduction has no affect on hp.
HP = Torque ft lbs x rpm / 5252

Engine PTO HP
20hp @6000 rpm = 17.5 ft lbs torque
THEN:
Gear reduction 2:1
6000 rpm/2 = 3000 rpm
17.5 x 2 = 35 ft lbs torque
RESULT:
PUMP INPUT SHAFT
35 ft lbs @ 3000 rpm = 20hp

20hp before the gear reduction - 20hp after the gear reduction.

Hydraulic HP requirement is the same regardless of reduction.
Its all about GPM at rpm you want.

 

this is going to be one of the greatest math battles in history lol

 

Good Article for choosing a Hyd Pump for that Type of Dyno.

https://yourdyno.com/choosing-the-right-hydraulic-pump/

 

Gear reduction has nothing to do with HP. It has to do with pump flow.

Look at the equation where I had it outlined in RED. - He is figuring gallons based on ENGINE rpm not PUMP rpm - Thats why the .258 reduction factor is there.
The overall HP equation does not change.

Very simple math every engine guy should already know shows gear reduction has no affect on hp.
HP = Torque ft lbs x rpm / 5252

Engine PTO HP
20hp @6000 rpm = 17.5 ft lbs torque
THEN:
Gear reduction 2:1
6000 rpm/2 = 3000 rpm
17.5 x 2 = 35 ft lbs torque
RESULT:
PUMP INPUT SHAFT
35 ft lbs @ 3000 rpm = 20hp

20hp before the gear reduction - 20hp after the gear reduction.

Hydraulic HP requirement is the same regardless of reduction.
Its all about GPM at rpm you want.

Each Size HYD PUMP can only be turned X Amount of RPM = X Amount of PRESSUE in (PSI) = X Amount of HP in Direct Drive as I said!

These Small Hyd Pumps have a 3000rpm to 3900rpm Range. it seems to be their MAX RPM RANGE their used at.

To figure HP made from PSI using ENGINE'S that are being turned at Higher 5500rpm to 7500rpm you need to use a Belt/Gear Reduction.

Like if your HYD Pump only has a Max 3000rpm Duty Cycle as you show and used a 2.0 Belt/Gear RATIO as you show is only good for 6000rpm Engine!

Were not Converting Known 20hp PTO Shaft Torque/hp, were Converting HYD Pump PSI @ different rpm to HP. These Small Honda/Clones are 6hp-12hp@3600rpm don't need a Big Pump. HP/Torque made goes up exponentially per + Amount of rpm used lets say +250rpm = 1.2hp in the Power Band. Like the 250 Type 247 is rated 12hp@5500rpm and we know it's probably less. So at 5250rpm is -1.2hp = 10.8hp, at 5000rpm -2.4hp = 9.6hp, etc!

As you said earlier: Don't think it works that way - could be wrong

The Horsepower formula in the chart is
Hp = GPM x Pressure /1714
67.2 hp x 1714 / 3200lbs = 36 GPM. <--- But his Pump only makes 6.6gpm@3600rpm.

The gearing RPM conversion in the video was to determine the GPM flow at various rpms.
His pump was rated at 1.52 cubic inch per revolution. So he needed the gearing to figure Engine RPM vs Pump rpm to get GPM.

At common engine 3600rpm - his pump is putting out
(3600rpm x .278) x 1.52ci /231 = 6.6gpm
To figure HP at 3600 rpm Multiply 6.6 GPM and pressure from gauge.

Going to get tricky doing a full rpm dyno sweep - maybe that is where software is coming from. <--- Yep as I said.
If engine rpm is 3600 the pump is making 6.6 GPM
Then at say 2500 rpm the pump is making 4.6 GPM
And at 4200 rpm the pump is making 7.7 GPM <--- These Hyd Pumps seem to use 3000rpm to 3900rpm Max

So at every engine rpm you want to look at - you need to change the calculation. <--- Yep, and you have to Multiple the HP@rpm by the Ratio used.
HP= (GPM@RPM) x PSI / 1714

 

This whole conversation started because earlier you said two things

"1) I'm mainly interested in the 25hp to 40hp Engine range for now."
"2) At 1:1 at 12gpm, 3200psi, 3000rpm = 22.4hp
At 2.0 at 12gpm, 3200psi, 3000rpm = 44.8hp
At 3.0 at 12gpm, 3200psi, 3000rpm = 67.2hp"

I was attempting to show you where you were mistaken - gear reduction does not change
MAX HP that can be measured. (Your 22.4 - 67.2)

Now you are saying we are not using PTO shaft Torque/HP numbers - only converting Pump PSI @ rpm to HP

Since you are confused - on a dyno there is an ENGINE. It has a PTO shaft that transmits its HP/Torque through that shaft. There is also reduction system using a big and little gear.

I am sorry you were confused by My 20hp EXAMPLE. I used 20hp and 6000 rpm because I thought the math would be easy for you to understand - I was Wrong.

Since you are no longer interested in 65hp engines - I'll show you again why your assumption that Max HP that can be measured changes with gear reduction 1:1, 2:1, 3:1 is wrong.

Now that you are focused only on 12Hp engines. I'll use those more complicated numbers.

PTO 12hp @ 5500rpm = 11.5 ft lbs
Gear Reduction 5500 to 3000rpm = 1.83
Torque at Pump 11.5 x 1.83 = 21 ft lbs
Therefore Pump must be sized for
3000 rpm x 21 / 5252 = 12 hp

12HP at engine and 12hp at pump - REGARDLESS of reduction .

As I said earlier - based on my dyno experience - you do not want to size your pump based on MAX PSI and MAX RPM unless you are POSITIVE you know your ENGINE HP/RPM numbers.
If you are positive - why do you need a DYNO?

Buy an OVERSIZED pump operating below max PSI and gear reduced for less than max pump rpm at your estimated ENGINE RPM / HP

 

Premade HYD Hose comes in different psi and different Lengths not overly expensive.

 

There are Digital Hyd Gauges which I think is better than what he used, but are more expensive.

 

This whole conversation started because earlier you said two things

"1) I'm mainly interested in the 25hp to 40hp Engine range for now."
"2) At 1:1 at 12gpm, 3200psi, 3000rpm = 22.4hp
At 2.0 at 12gpm, 3200psi, 3000rpm = 44.8hp
At 3.0 at 12gpm, 3200psi, 3000rpm = 67.2hp"

====> Post #1

This DIY Dyno was built for Testing Small Honda/Clone 4 Strokes. To do these Old 12hp to 50hp Sled Engines you just need a bigger Hydraulic Pump and Pressure Gauge. So were not Testing Honda/Clone Singles 6-9hp, things in the list are going to be upgrade for our 12hp to 70hp Sled and Ultralight Engines.

Everybody is going to have different Wants and X amount of $$$ they want to spend when it comes to Max hp to Dyno. So we have to ascertain Pump Sizes needed, say 5-40hp, 5-70hp, 5-100hp.

Post #4
I have looked at using a Gen Head. Most of these Old Sled Single Cylinder Motors were in the 12hp to 36hp Stock. In Racing form maybe up to 65hp if turning higher rpm. Ultralight Engines use Max 6500rpm. So the 277UL, 377UL, 447UL, 503UL, are Max 50hp with a Muffler, but can be up to 70hp with a Good Tuned Pipe.

Post #6
I'm still doing research, but If I understand it right, you can use different Belt/Gear Ratios. At 1:1, Yes the Hyd Pump is good up to X amount of Hp. Like this $120 Hyd Pump on eBay has a 12gpm, 3200psi, at 3000rpm rating.

Which at 1:1 Ratio is good for 22.4 hp. You input the correct ratio used in the Software.

For these Old Sled Engines and Ultralight Engines were looking at 12hp to 65hp and using 5500rpm to say 7500rpm. <===

I was attempting to show you where you were mistaken - gear reduction does not change
MAX HP that can be measured. (Your 22.4 - 67.2)

===> In one of the Videos they talked about using a Ratio for figuring the hp. I'll have to go back and watch them again. <===

Now you are saying we are not using PTO shaft Torque/HP numbers - only converting Pump PSI @ rpm to HP.

====> Yes, were Measuring the Engine PTO Shaft Torque and converting that to hp. We know the Factory rated Spec's. Were trying to Size the Hyd Pump to reflect that hp/torque. You do have to Size that Hyd Pump for Higher hp, like the Hyd Pump they used in the Video was for Honda/Clone 4 Stroke Singles in the 6-9hp range and was 3,600psi, 6.6gpm, 13.9hp. Their HYD Pump they used 6.6gpm about $70. The bigger one I showed $120, 12gpm, 3200psi, 3000rpm = 22.4hp! <====

Since you are confused - on a dyno there is an ENGINE. It has a PTO shaft that transmits its HP/Torque through that shaft. There is also reduction system using a big and little gear.

I am sorry you were confused by My 20hp EXAMPLE. I used 20hp and 6000 rpm because I thought the math would be easy for you to understand - I was Wrong.

====> No, I'm not confused. They didn't show how they figured the 1.52 Flow Rate. They did show the Gear ratio used. <====

Since you are no longer interested in 65hp engines - I'll show you again why your assumption that Max HP that can be measured changes with gear reduction 1:1, 2:1, 3:1 is wrong.

====> I have already stated "For these Old Sled Engines and Ultralight Engines were looking at 12hp to 65hp and using 5500rpm to say 7500rpm. <===

Now that you are focused only on 12Hp engines. I'll use those more complicated numbers.

PTO 12hp @ 5500rpm = 11.5 ft lbs <==== Factory Rating but we know it's not exact is it! Companies Round up Numbers!
Gear Reduction 5500 to 3000rpm = 1.83
Torque at Pump 11.5 x 1.83 = 21 ft lbs
Therefore Pump must be sized for
3000 rpm x 21 / 5252 = 12 hp

12HP at engine and 12hp at pump - REGARDLESS of reduction.

=====> I can agree with your Numbers above, but it doesn't solve the Problem on what Size of Hyd Pump we need. Like you said, you don't Size the Pump for your known Factory hp@rpm! You have to Factor in the Modifications you want to make like using a Bigger Carb, Higher CR, Porting, and higher rpm you may want to turn the Engine, too using a better Muffler or a Tuned Pipe. Like taking a 250 Type 247 12hp and do all the Bells & Whistles at it similar to a Blizzard 246 Single which I have seen 24hp and 29hp listed. A Polini 250 is 36hp@8000rpm.

Rotax 250 Type 247, 246.8cc/7cc= 35.2hp, 246.8/8cc = 30.85hp, 246.8cc/9cc= 27.4hp. <===

As I said earlier - based on my dyno experience - you do not want to size your pump based on MAX PSI and MAX RPM unless you are POSITIVE you know your ENGINE HP/RPM numbers.
If you are positive - why do you need a DYNO?

====> The same reason anyone Dyno's their Engine to check Factory Rating and to see what extra hp is made at different rpm from Modifications you want to make like using a Bigger Carb, Higher CR, Porting, and higher rpm you may want to turn the Engine, too using a better Muffler or a Tuned Pipe. A Racer might go direct from Stock 8.0cr to 14.0-16.0cr, where as a Sledder might go 8.0cr to 11.0cr for a Hot Trail Sled. Rotax Singles Stock went from 12hp to 36hp. Like I said in Racing form probably up to 55hp. The Yamaha 292 Single was 70hp@9200rpm per Aaens website. <====

Buy an OVERSIZED pump operating below max PSI and gear reduced for less than max pump rpm at your estimated ENGINE RPM / HP

Duh, that's what I'm trying to ascertain. Like I said, I'm still researching this! But I'm also trying to give people other examples of what might Work for their wants. A person interested in just Dynoing Old Rotax Singles is looking at 12hp to 36hp range, but up to 70hp if into Racing them The original Design was for just 6-9hp Honda/Clones 13.9hp Max with a Target Price to build around $500. The Pump Size is the main thing that needs to be changed for different hp ranges. Hyd Hose whether 2000psi to 5000psi Cost about the same. Since not many People are even into Racing Sleds today and Old Singles ranged 12hp to 36hp a Pump for up to 45hp would probably suffice. Even with need ing a Bigger Hyd Pump, I think it can be built for $500 or less. It's to Cold to roam Junk Yards, but I bet I can find most of what's needed in there. The next group might want one for up to 80hp, the next group might want up to 120hp, etc. Old Small Twins ranged 20hp to 50hp, Old large Twins went up to 85hp. A Pump for 100hp would probably cover 99% of these Older 60's to 2000 Engines. In the 2000's we seen the demise of the 277F, 380F, 440F, 503F, and in the 90's we seen the demise of the 470LC, 500LC, 521LC, 617LC, 670LC. In the late 90's to 2000's we lost the 277UL, 377UL, 447UL, 503UL, 532UL, 618UL.

All of these Hyd Pumps are going to have to use some form of Reduction Ratio.

Some Hyd Pumps are rated in MPa. Like MPa 21 = PSI 3,045.8.

https://online-calculator.org/conversion/mpa-to-psi.php

On a Dyno your only running these Hyd Pumps up a little past your desired Max rpm then going right back to idle in Seconds to do that. So you ought to be able to run them up to the Max Intermittent Pressure of 3600psi, using 4000psi Hyd Hoses.

3,200psi, 12gpm, 22.4hp
3,600psi, 12gpm, 25.2hp

3,900psi, 12gpm, 27.3hp

That $120 Hyd Pump.

Max 3200psi Working Pressure

Max 3600psi Intermittent Pressure

Max 3900psi Pressure

 

Duh, that's what I'm trying to ascertain. Like I said, I'm still researching this! But I'm also trying to give people other examples of what might Work for their wants. A person interested in just Dynoing Old Rotax Singles is looking at 12hp to 36hp range, but up to 70hp if into Racing them The original Design was for just 6-9hp Honda/Clones 13.9hp Max with a Target Price to build around $500. The Pump Size is the main thing that needs to be changed for different hp ranges. Hyd Hose whether 2000psi to 5000psi Cost about the same. Since not many People are even into Racing Sleds today and Old Singles ranged 12hp to 36hp a Pump for up to 45hp would probably suffice. Even with need ing a Bigger Hyd Pump, I think it can be built for $500 or less. It's to Cold to roam Junk Yards, but I bet I can find most of what's needed in there. The next group might want one for up to 80hp, the next group might want up to 120hp, etc. Old Small Twins ranged 20hp to 50hp, Old large Twins went up to 85hp. A Pump for 100hp would probably cover 99% of these Older 60's to 2000 Engines. In the 2000's we seen the demise of the 277F, 380F, 440F, 503F, and in the 90's we seen the demise of the 470LC, 500LC, 521LC, 617LC, 670LC. In the late 90's to 2000's we lost the 277UL, 377UL, 447UL, 503UL, 532UL, 618UL.

All of these Hyd Pumps are going to have to use some form of Reduction Ratio.

Some Hyd Pumps are rated in MPa. Like MPa 21 = PSI 3,045.8.
https://online-calculator.org/conversion/mpa-to-psi.php

On a Dyno your only running these Hyd Pumps up a little past your desired Max rpm then going right back to idle in Seconds to do that. So you ought to be able to run them up to the Max Intermittent Pressure of 3600psi, using 4000psi Hyd Hoses.
3,200psi, 12gpm, 22.4hp
3,600psi, 12gpm, 25.2hp
3,900psi, 12gpm, 27.3hp

That $120 Hyd Pump.
Max 3200psi Working Pressure
Max 3600psi Intermittent Pressure
Max 3900psi Pressure

Little to "Ascertain". - It has been identified already!

1) Gear reduction ratio has NOTHING to do with pump MAXIMUM HP capability
It has been shown twice using mathematics.
And can be shown again and again.

2) Figure required reduction by using this complicated equation
Max engine speed / Max pump speed = required reduction.
EXAMPLE - DO NOT USE FOR YOUR ENGINE - THIS IS ONLY AN EXAMPLE
9000rpm engine / 3000 rpm max pump speed = 3.0 reduction required.

3) Know what is wanted before selecting a pump and building a dyno
12HP, 36hp, 45HP, 80hp,100hp, 120HP PICK SOMETHING! And build it.

4) If not comfortable with MATH - online calculator is available for MAX HP for any pump.
https://yourdyno.com/choosing-the-right-hydraulic-pump/

5) When researching pumps - write down the following information for each pump.
Max RPM,
Max PSI,
Pump Cubic in or ML per revolution,
GPM @RPM if given,
And Finally PRICE
Use the numbers in the online calculator or a spreadsheet or phone calculator or pencil and paper.

6) Buy a pump bigger than thought is needed because real world dyno testing an engine is not a spreadsheet.

7) EXCEED MANUFACTURES RATINGS AT YOUR OWN RISK - Real World Dyno Testing is not a game. - Things break and people get hurt.
.

 

EXAMPLE OF WHY OVERSIZED PUMP RECOMMENDED

The 503 engine power curve has been dyno verified and the results published.
50hp engine with broad power band producing close to 50 hp over a large rpm range.

Because of the nature of the proposed hydraulic dyno - you CANNOT size everything based on ONE RPM. Need to consider the possible HP/RPM combinations over the total test range.

In this EXAMPLE - ONLY AN EXAMPLE - 7000rpm is chosen to allow a 250rpm overshoot range on top of the 6750rpm top speed to be measured.

In this EXAMPLE - ONLY AN EXAMPLE - the pump is near MAX PSI from 5750 to 6250 RPM

 

=========================

Looking back at this thread. Your Example has me confused. I agree you should have a Hyd Pump bigger than you think your Max hp you will be Dynoing for. You also need to Plan for Higher rpm. Aviation use today is Max 6500rpm, so 7500rpm for Sled use. While it would be interesting to Dyno some of the Bigger Engines like the 470/462UL, 521/532UL, 580, 582, 583, 582UL, and the 617/618UL, and the 670 at higher 77650rpm that would require a much Larger Hyd Pump that pushes up the Price! For me, it started out thinking of just the Old Singles 12-36hp and the 277UL where even Max hp would be 38hp, so a Hyd Pump for 40-45hp would suffice. But I can see myself wanting to Test some 377UL/377F, 447UL/440F, and 503UL/503F Engines at 6500rpm for Aviation use and up to 7500rpm for Sled use. So 12hp to 70hp Range.

If HP = GPM x Pressure/1714. Your Example doesn't make sense to me.

HGP AL78K -B02-220R
MAX 3000 RPM
MAX Psi 2900
Max GPM 28.56
You Say: 56.8 hp.

28.56 x 2900 = 82,824 / 1714 = 48.322 hp.

Now the 503UL Dual Carb was rated 49.6hp@6500rpm, actually Dynoed 49.8hp@6250rpm. So I would assume this Hyd Pump is to Samll.

At the bottom of your list:
Chief SKU: 252179
MAX 2800 RPM
MAX Psi 3625
Max GPM 35

You Say: 87.1hp.

35 x 3625 = 126,875 / 1714 = 74.022 hp.

Bottom Hyd Pump. Using your example.
=SUM(3.11*2800/231)*3625/(1714*0.93) = 85.7276 hp vs your 87.1 hp. Regardless that Pump seems to be the best choice so far.

This Hyd Pump would cover all of the Singles and the Small Twins up to a 503F at 7500rpm.

A 503UL 496.9cc/7cc= 70.9hp@6500rpm is possible.