The S.U.R.E. project

[SSW1]

http://www.sim-outhouse.com/sohforums/attachment.php?attachmentid=59251&stc=1
Those who use the SSW F-104 S or the SSW FRF-104 G will find interesting the pages of the SURE project (https://www.dropbox.com/s/pp9jdqsv14xumy2/The%20Sure%20Project.pdf?dl=0), this document was for the SSW one of the most used to build the flight model of the SSW "zipper" of which the first version was released 6 years ago, today we are counting hundreds of satisfied users, thanks to everyone.
Thanks to Diego
/SSW

[Bjoern]

Very interesting read; thanks for the upload!

[warchild]

Excellent read. Thank you..

One thing that is tripping me up about it is the statement that the F-104 has a high wing load ( weight/wing area ). That seems simple enough on the face of it, but that wing ws taken directly from the Bell X-3 which NACA plainly stated was a high fuselage loading. It was that high fuselage loading that caused the adverse pitch at transonic speeds while rolling, and its known that although the f-104 made use of lessons learned from th X-3 ( with the T-Tail configuration ) it also had some "interesting" issues with adverse yaw. What would be your take on this change in terminology??

Pam

[Sundog]

I've never even heard the term fuselage loading, although, in the way they are referencing it to the X-3, I think they would be talking about the aerodynamic loads as the inertial roll coupling diverges and the aerodynamic loads increase on the fuselage. As the aerodynamic loading along the fuselage isn't trivial given it has a lot of area ahead of and behind the center of mass and that greatly affects the stability derivatives.

I only encountered this type of loading in stability and control. For instance, when an aircraft yaws, many people just consider the area of the vertical tail, when what you really want is the control volume of the vertical tail (control volume of the vertical tail is vertical tail area multiplied by the longitudinal distance between the tail's aerodynamic center and the center of mass, which is a measure of control power). However, when you think about an aircraft yawing and remember that an aircraft rotates about it's center of mass, the fuselage is starting to turn sideways to the airflow. So the air hitting the side of the aircraft into the relative wind (The airflow coming at the aircraft in an aircraft frame of reference) is a dynamic pressure load on the fuselage, whereas on the leeward side, opposite the relative wind, you can develop suction loads.

The part of the fuselage ahead of the center mass wants to destabilize the aircraft; it wants to turn it away from the direction it is moving. The part of the fuselage behind the center of mass wants to stabilize the aircraft, make it weather vane into the direction it is moving. However, it is also in the wake of the wing and in a more turbulent region, so it may not develop loads as powerful as those at the nose; it depends on the design. As noted above, with a fuselage as long as the X-3's, the loads aren't trivial, especially when taken into account with the mass distribution and the small aerodynamic surfaces (small dampers).

So my guess is they were looking at the aerodynamic load distribution down the fuselage as it diverged more and more away from the velocity vector. I can see it in my head, but I'm not sure my words are conveying it so well. let me know and I can probably make some drawings this week to show what I'm talking about.

[fliger747]

Both can be true.

Certainly the wing surface divided by weight of the aircraft gives a wing loading, which is in relative terms is high.

HH Hurd, Aerodynamics For Naval Aviators has a discussion on Inertial coupling beginning on page 315. This tomb is available free on line for those interested. In essence the linear distribution of mass along the fuselage combined with low roll inertia can cause gyroscopic roll forces. This is exacerbated by inclination of the mass axis at higher angles of attack.

Though roll inertia is low, the ailerons also have a short lever arm and need a larger degree of deflection and tend to create an adverse yaw which combines with the roll coupling inertial effects.

Inconvenient aerodynamic truths have led to development of patches from yaw dampers on to full fly by wire controls of today.

T

[warchild]

I've never even heard the term fuselage loading, although, in the way they are referencing it to the X-3, I think they would be talking about the aerodynamic loads as the inertial roll coupling diverges and the aerodynamic loads increase on the fuselage. As the aerodynamic loading along the fuselage isn't trivial given it has a lot of area ahead of and behind the center of mass and that greatly affects the stability derivatives.

I only encountered this type of loading in stability and control. For instance, when an aircraft yaws, many people just consider the area of the vertical tail, when what you really want is the control volume of the vertical tail (control volume of the vertical tail is vertical tail area multiplied by the longitudinal distance between the tail's aerodynamic center and the center of mass, which is a measure of control power). However, when you think about an aircraft yawing and remember that an aircraft rotates about it's center of mass, the fuselage is starting to turn sideways to the airflow. So the air hitting the side of the aircraft into the relative wind (The airflow coming at the aircraft in an aircraft frame of reference) is a dynamic pressure load on the fuselage, whereas on the leeward side, opposite the relative wind, you can develop suction loads.

The part of the fuselage ahead of the center mass wants to destabilize the aircraft; it wants to turn it away from the direction it is moving. The part of the fuselage behind the center of mass wants to stabilize the aircraft, make it weather vane into the direction it is moving. However, it is also in the wake of the wing and in a more turbulent region, so it may not develop loads as powerful as those at the nose; it depends on the design. As noted above, with a fuselage as long as the X-3's, the loads aren't trivial, especially when taken into account with the mass distribution and the small aerodynamic surfaces (small dampers).

So my guess is they were looking at the aerodynamic load distribution down the fuselage as it diverged more and more away from the velocity vector. I can see it in my head, but I'm not sure my words are conveying it so well. let me know and I can probably make some drawings this week to show what I'm talking about.


Thanks for the quick response :)..

I think you and I share the same picture. I'm pulling my reference from the nasa statement:

"NACA pilot Joseph A. Walker made his pilot checkout flight in the X-3 on August 23, 1954, then conducting eight research flights in September and October. By late October, the research program was expanded to include lateral and directional stability tests. In these tests, the X-3 was abruptly rolled at transonic and supersonic speeds, with the rudder kept centered. Despite its shortcomings, the X-3 was ideal for these tests. The mass of its engines, fuel and structure was concentrated in its long, narrow fuselage, while its wings were short and stubby. As a result, the X-3 was "loaded" along its fuselage, rather than its wings. This was typical of the fighter aircraft then in development or testing. These tests would lead to the X-3's most significant flight, and the near-loss of the aircraft."

Which i retrieved from the article at:

https://www.nasa.gov/centers/armstrong/news/FactSheets/FS-077-DFRC.html

The X-3s nose would pitch up twenty degrees with the rudder centered and ailerons abruptly applied at trans-sonic speeds. The problem plagued Nasa for some time, and they finally found it was slightly abated when they raised the horizontal stabilizer upwards by eleven inches.

Now, I've got another document from nasa that states that the x-3 was the "proof of concept" for the F-104 ( their statement, not mine ) and that the lessons learned from the X-3 went directly into the f-104: hence the similarities in design, with the biggest exception being the F-104s T-Tail. Yes, the wings have a nearly identical aspect ratio..

I suppose what i'm hoping to learn, is how the T-tail as well as the single centerline engine change the adverse yaw characteristics from the X-1s and X-3s nose up tumbling spin. What is adverse yaw in the F-104 like??

I've watched several videos today where f-16s in a left bank spun out to the right, and cessnas spun in the opposite direction as well, but even though those are exceedingly dangerous, theyre nothing like what the planes of the early to late 1950s experienced, and i'd like to understand how we got from the X-3s behaviour, to where we're at today..

Pam

[fliger747]

Something not generally realized is the considerable internal gyroscopic and inertial forces created by a high RPM spinning of a turbine engine, I would expect a single might be worse than a twin.

[warchild]

Both can be true.

Certainly the wing surface divided by weight of the aircraft gives a wing loading, which is in relative terms is high.

HH Hurd, Aerodynamics For Naval Aviators has a discussion on Inertial coupling beginning on page 315. This tomb is available free on line for those interested. In essence the linear distribution of mass along the fuselage combined with low roll inertia can cause gyroscopic roll forces. This is exacerbated by inclination of the mass axis at higher angles of attack.

Though roll inertia is low, the ailerons also have a short lever arm and need a larger degree of deflection and tend to create an adverse yaw which combines with the roll coupling inertial effects.

Inconvenient aerodynamic truths have led to development of patches from yaw dampers on to full fly by wire controls of today.

T

Thank you for clarifying that. That bold part above is exactly what i wasnt envisioning.. I'm amazed that book is so affprdable too.. Will be getting it friday :)..
Thanks again Tom.. Really helps a lot..
Pam

[warchild]

Something not generally realized is the considerable internal gyroscopic and inertial forces created by a high RPM spinning of a turbine engine, I would expect a single might be worse than a twin.

And that would be due to the nature of the forces from dual engines balancing themselves out. I really wish i had the grasp of language to describe what i believe your saying, but i'm afraid I dont. Still, i can sort of see the circular forces of two engines dividing the aircraft more or less in half, whereas the forces from a single engine would be applied equally to the entire length of the engine effecting the entire aircraft, much the way a propeller effects adverse yaw from the front of the plane in that cessna i watched..

As the axis of the engine spins, it produces a circular force in the opposite direction of rotation, equal to the force it is developing from the spin. this would cause the plane to want to rotate away from the direction of the engines spin, but is countered by control surfaces and the mass of the aircraft being greater than the force of that spin??

P>S> Awesome PDF.. Thanks Tom..

[Sundog]

Basically, how we got from there to here, is a history of mostly aero-propulsion (more thrust, less weight), structures (less weight), aerodynamics (less drag, more lift).

If you look at the early supersonic jets, many of them had small wings and long fuselages. This was due to the very low thrust, relatively speaking, and low thrust to weight ratios of the earlier jet engines. A long fuselage results in a high fineness ratio, which greatly aids lowering supersonic drag. Since lift is directly related to speed, you don't need a big wing when going fast to stay in the air, so they went with small wings, based on area, which also reduces weight, to keep drag low. Of course, all of that also leads to high landing and take-off speeds, which many of the early jets suffered from as well. There was also the problem of them getting behind the power curve at those speeds, etc.

But as engines became more powerful, you could go with a bigger wing, since the drag was offset by the excess power. In fact, one of the the greatest break troughs in jet engine design in the 50's was the J-79. I don't think a lot of people realize what a game changer that design was, as it's older and we sort of take it for granted now. It ended up being a very bulletproof design.

I should note that requirements also come into play. For instance, look at the F-104 and the F-11F-1F (I'm glad the Navy finally dropped that designation system!) Super Tiger. Both were double sonic fighter designs, but the F-104 was very unforgiving with it's small wing and t-tail. The West Germans regretted not buying the Super Tiger when they had the chance, but by then it was too late. Granted the F-104 had phenomenal acceleration, and was the only plane that could hang with a Blackbird right after take-off, IIRC. But the Super Tiger was more forgiving and had much lower circuit speeds with it's larger higher aspect ratio wing and was quite maneuverable, in order to meet the U.S. Navy requirements.

Anyway, as the timeline moves on, you see jets now being designed for maneuverability and agility, not just interception, with the teen series fighters, and you start getting aircraft with higher T/W engines and larger wing areas. The result is, you get more damping area (wings and tail surface areas) for a given mass. Also, with all of their excess thrust, high alpha started getting more attention. That's because it is a high drag region, which really wasn't usable until they received the ability to make the high T/W power plants. Making aircraft being able to fly in high alpha regions lead to better spin resistance, which was also the reason many designs moved to twin tails. In a spin, the fuselage usually blanks out the vertical tail, so it can't stop the spin. But having twin tails usually means the tail that is on the leading side of the spin remains effective. The original F-16 design had twin tails, which is part of the reason it had the two side extensions that the horizontal tails and air brakes are supported on. But it went with a single tail due to interference from the LERX vortices with twin tails.

Also, with the introduction of fly-by-wire flight control systems, they could also keep the pilots out of flight conditions that could lead to problems. Of course, that's only as good as the programming and one of the reasons new designs with these flight control systems require so much time to develop; well, that and the instability, automatically configuring for different flight modes, etc.

But, you get the idea. Power; lots and lots of excess thrust. That's why we can make planes perform so well and, when combined with advanced aerodynamics and flight controls, make them do just about anything. In fact, one of the greatest flight displays I have ever seen was on an Aviation Week video, which isn't on YouTube (Darn), of the X-31 display at the Paris Airshow in the 90's. Granted, it was just an X-Plane, but that was one of the most amazing demonstrations I've ever seen.

The Fighter that replaces the F-22 (F-X) will use three stream variable bypass engines (Optimizing the bypass ratio, for thrust and fuel efficiency) and will also differ from current engines in that it will be able to generate quite a bit more electrical power, since the future combat designs will be very system intensive and most likely be armed with laser defense systems and all sorts of ECM, etc.

[Sundog]

Something not generally realized is the considerable internal gyroscopic and inertial forces created by a high RPM spinning of a turbine engine, I would expect a single might be worse than a twin.

Which, it seems, is why most modern military engines are twin spool, with each spool rotating in opposite directions, to make the gyroscopic forces net zero, or something close to it.

[fliger747]

Some discussion to counter rotating spools as to an increase in thermodynamic efficiency. In Modern aircraft fly by wire would erase any perceived effects. However in aircraft such as the F104 this might be an important aspect.

As far as large aircraft, neither the 747-400 or the Intercontinental-8 which had very different engines had any noticeable difference in takeoff or power change in my experience with them. By contrast the C-130 did have noticeable if not horrible torque effects.

Interesting!

[warchild]

Welll, We've got that RF-8G project coming up, and i want to make sure I do my part right. That means, it uses coupled yaw; takes into account weathervaning and roll pitch and yaw stability, and gyroscopic effects; none of which I'm an expert on. At least now, thanks to your generosity, i have an idea of what i'm dealing with and where to look for the remaining pieces so that i can do my best, and better. Your all, very much worth at least that much from me. Thank you..

[Bjoern]

Something not generally realized is the considerable internal gyroscopic and inertial forces created by a high RPM spinning of a turbine engine, I would expect a single might be worse than a twin.


Some discussion to counter rotating spools as to an increase in thermodynamic efficiency. In Modern aircraft fly by wire would erase any perceived effects. However in aircraft such as the F104 this might be an important aspect.

As far as large aircraft, neither the 747-400 or the Intercontinental-8 which had very different engines had any noticeable difference in takeoff or power change in my experience with them. By contrast the C-130 did have noticeable if not horrible torque effects.

Interesting!

Gyroscopic effects in jet engines are (apparently) only relevant if the lifting surfaces can't counteract them. With a bit of quick research, even in a Starfighter, there were only very minor gyroscopic effects when accelerating the engine from idle to MIL or back or when at very high altitude (NF-104).
Another thing I found is that the Pegasus in the Harrier has counter-rotating spools to cancel out as much gyroscopic effects as possible to make it easier to keep in a hover.

As for commercial aircraft, the comparatively large lifting and control surfaces in relation to engine dimensions minimize any gyroscopic effects. Not even a GE90 powered 777-300ER should experience notable gyroscopic effects.

As for the C-130, I take that all propellers and engines rotated in the same direction. Add the large props to the equation and you've got sizeable moment arms.
Torque and gyroscopic effects are the reason why the A400M has this horribly complicated setup of counter rotating props on each wing.




And that would be due to the nature of the forces from dual engines balancing themselves out.

No, they don't. Since counter-rotating shafts or engines are more complicated to develop and maintain (due to flow paths and keeping spare part inventories), engines generally only rotate in a single direction, with the exception of applications where torque and gyroscopic effects were absolutely necessary to be minimal (see Harrier and A400M example above).




But as engines became more powerful, you could go with a bigger wing, since the drag was offset by the excess power. In fact, one of the the greatest break troughs in jet engine design in the 50's was the J-79. I don't think a lot of people realize what a game changer that design was, as it's older and we sort of take it for granted now. It ended up being a very bulletproof design.

Eventually, yes. Not sure what the story was for other users or applications, but the Luftwaffe's Starfighter accident rate markedly improved after MTU changed the nozzle actuation system from fuel-driven to hydraulic and implemented an emergency closing system.
Starfighters using the J79-GE-11 sometimes suffered from afterburner malfunctions, leaving the nozzle wide open and subsequently without the necessary thrust to keep flying. With the modification, the emergency closing of the nozzle at least made it convergent enough to recover enough thrust to keep flying and limp home.



I should note that requirements also come into play. For instance, look at the F-104 and the F-11F-1F (I'm glad the Navy finally dropped that designation system!) Super Tiger. Both were double sonic fighter designs, but the F-104 was very unforgiving with it's small wing and t-tail. The West Germans regretted not buying the Super Tiger when they had the chance, but by then it was too late. Granted the F-104 had phenomenal acceleration, and was the only plane that could hang with a Blackbird right after take-off, IIRC. But the Super Tiger was more forgiving and had much lower circuit speeds with it's larger higher aspect ratio wing and was quite maneuverable, in order to meet the U.S. Navy requirements.

Navy requirements don't quite match the requirements of fighter bomber missions over the European continent. Bribery and questionable payload aside, the Luftwaffe wanted fighter bomber and anti shipping capability when they ordered the F-104. One of the Starfighter's virtues is high wing loading and low drag (and the comparatively sophisticated radar), two aspects that made it ideal to get in fast below the OPFOR's radars (low drag), deliver the ordnance without being rattled by every gust of wind (high wing loading).
As a bonus (and bribery aside), the Starfighter was the first multinational jet fighter project due to the Military Assistance Program and being used and produced by various NATO members.


In fact, one of the greatest flight displays I have ever seen was on an Aviation Week video, which isn't on YouTube (Darn), of the X-31 display at the Paris Airshow in the 90's. Granted, it was just an X-Plane, but that was one of the most amazing demonstrations I've ever seen.

Is that a snippet of the demo?
https://www.youtube.com/watch?v=OcArP5bYk6s

Other than that, there's quite a bit of footage from the test flights on Youtube.

Would be cool to have one for flight simming, but it'd need some external module magic to provide3D thrust vectoring capability without outright putting it into the flight dynamics.

[fliger747]

https://www.faa.gov/regulations_policies/handbooks_manuals/aviation/media/00-80T-80.pdf

PDF freebee of HH Hurd Aerodynamics for naval Aviators.

It is of course at the limits of the aerodynamic envelope that we do run out of control in some manner and things like turbine engines gyroscopic effects can be important. High AOA, low speed, high altitude with poor dampening and ACM are a few possibilities.

T

[fliger747]

http://www.sim-outhouse.com/sohforums/attachment.php?attachmentid=59262&stc=1

From HHHurd Illustration of roll coupling

[warchild]

http://www.sim-outhouse.com/sohforums/attachment.php?attachmentid=59262&stc=1

From HHHurd Illustration of roll coupling

This is exactly what i thought, and exactly what you said regarding one large engine instead of two smaller engines side by side.. Yes, I know that the end result is the same.

Bjoern:
What I was saying is that if you put two engines side by side, each developing the exact same amount of centripetal force, the two rotational ( centripetal ) forces will cancel each other out at the point where they meet in the middle, and in this case the middle is the longitudinal axis of the aircraft. However, I see what your saying as well as the twin engine configuration does not get canceled out as each engine is still developing a rotational force. However, due to the interferance effect where the two rotational forces meet, the region effected by that rotational force becomes oblong, encircling both engines and is no longer a pure rotational force. Also, since two engines side by side would have individual masses smaller than a single large engine, they would each develop a weaker rotational force than the single large engine, and that force would be further weakened by the rotational forces being canceled out where the forces of the two engines counter each other. This of course also becomes mute, if the two engines are seperated by enough space that the two rotational forces no longer effect one another which in and of iteself creates a whole new can of worms to be considered..
Pam

[Bjoern]

What I was saying is that if you put two engines side by side, each developing the exact same amount of centripetal force, the two rotational ( centripetal ) forces will cancel each other out at the point where they meet in the middle, and in this case the middle is the longitudinal axis of the aircraft. However, I see what your saying as well as the twin engine configuration does not get canceled out as each engine is still developing a rotational force. However, due to the interferance effect where the two rotational forces meet, the region effected by that rotational force becomes oblong, encircling both engines and is no longer a pure rotational force. Also, since two engines side by side would have individual masses smaller than a single large engine, they would each develop a weaker rotational force than the single large engine, and that force would be further weakened by the rotational forces being canceled out where the forces of the two engines counter each other. This of course also becomes mute, if the two engines are seperated by enough space that the two rotational forces no longer effect one another which in and of iteself creates a whole new can of worms to be considered..

Centripetal force is not a factor since it acts radially. It only determines if the compressor disk stays in one piece or not.
The slipstream generated by the rotating disks and imposing force on parts attached to the casing (guide vanes, stators, struts, etc.; imagine a prop aircraft with a duct around the slipstream) is what transmits the torque. From the engine casing, the torque is then transmitted to the rest of the airplane.
Assuming a single torque/thrust pin from the casing and a low speed situation, e.g. takeoff, accelerating engines would transmit a force acting in the direction of rotation to that pin, which in turn tries to push the fuselage to the right. Both engines rotate in the same direction, so the forces are cumulative. If the right main gear shock absorber is soft enough, you'd see it compress during spool-up until a force counteracting the one transmitted from the engines can be generated. I most cases, the absorber springs back a bit, producing a counterforce that is then transmitted to the left absorber, producing a bit of rolling until the motion is dampened out due to a stabilized engines and spring dynamics.

I figure the effect of the torque is ultimately negligible on multi-engine aircraft since the landing gear or the aerodynamic surfaces damp out much of the initial momentum, but it is notable on small aircraft with big engines.

Certainly influenced by the runway condition, you can see the right wingtip dip a bit during spool-up on this F-16:
https://youtu.be/1Mwo15yOLwc?t=2m54s

It's much more notable on the Starfighter since it's also completely stationary (watch for the howl alone):
https://youtu.be/aKv9lsdln7E?t=35m23s


I hope that I'm not too far off with this, but that's what makes most sense to me.

[fliger747]

To clarify slightly, the main issue with a relatively weighty turbine assembly spinning at very high speed is mostly gyroscopic. By the aircraft maneuvering and changing the direction of the angular momentum of the spinning turbine wheels, gyroscopic force will tend to act as a result.

Because of the inter-turbine stators and tailpipe effects, generally the jet outflow will not have a large rotational aspect. Just as a personal observation, because of the large number of blades and the shrouding, even large bypass turbofans do not appear to have the swirling effect of a propeller.

Large 4 blade propellers also can have a significant destabilizing effect due to gyroscopic forces in maneuvering. Some issues for example were experienced in the upgrade to the Merlin in the Mustang and the larger/heavier four blade prop.

What we can do about all this stuff with only scanty information, who knows.

; )

[Sundog]

To clarify slightly, the main issue with a relatively weighty turbine assembly spinning at very high speed is mostly gyroscopic. By the aircraft maneuvering and changing the direction of the angular momentum of the spinning turbine wheels, gyroscopic force will tend to act as a result.

Because of the inter-turbine stators and tailpipe effects, generally the jet outflow will not have a large rotational aspect. Just as a personal observation, because of the large number of blades and the shrouding, even large bypass turbofans do not appear to have the swirling effect of a propeller.

Large 4 blade propellers also can have a significant destabilizing effect due to gyroscopic forces in maneuvering. Some issues for example were experienced in the upgrade to the Merlin in the Mustang and the larger/heavier four blade prop.

What we can do about all this stuff with only scanty information, who knows.

; )

It indeed has to do with the size of the rotating mass, it's distance from the center of mass, and the fact that jets generally have counter rotating rotors. Note, that most pilots who have flown contra-rotating props (Two props on the same axis turning opposite directions) haven't had to worry about gyroscopic affects when adjusting the throttle setting; I think one of the pilots flying the restored Seafire Mk.47 said it responded like a jet. In fact, when we (Plane Design) were developing the Spitfire, we were shocked at how much you could feel the gyroscopic affects of the propeller. IIRC, nose down it swung left and nose up it swung right; A P-51 would be the opposite, since it's propeller rotated in the opposite direction. As Andy Sephton (Former RAF Test pilot and, at that time, was still flying Spitfires and was our main FDE test pilot) explained to us, "This is a World War Two, high performance, high power fighter, not a Cessna."

[warchild]

I honestly think we're all saying th exact same thing here, just using different terms to define it. Bjoerns video of the F-104 certainly shows what we're discusing. Gyroscopic force is whats driving it and centripetal force is whats causing it.
No, Centripetal force is not glue that holds things together.. Here.. a grade school definition..

What is a centripetal force?A centripetal force is a net force that acts on an object to keep it moving along a circular path.

In our article on centripetal acceleration (https://www.khanacademy.org/science/physics/centripetal-force-and-gravitation/centripetal-forces/a/science/physics/centripetal-force-and-gravitation/centripetal-acceleration-tutoria/a/what-is-centripetal-acceleration), we learned that any object traveling along a circular path of radius rrrr with velocity vvvv experiences an acceleration directed toward the center of its path,

a=v2ra = \frac{v^2}{r}a=r
v2​a, equals, start fraction, v, start superscript, 2, end superscript, divided by, r, end fraction.

However, we should discuss how the object came to be moving along the circular path in the first place. Newton’s 1ˢᵗ law (https://www.khanacademy.org/science/physics/centripetal-force-and-gravitation/centripetal-forces/a/science/physics/forces-newtons-laws/newtons-laws-of-motion/a/what-is-newtons-first-law) tells us that an object will continue moving along a straight path unless acted on by an external force. The external force here is the centripetal force.

It is important to understand that the centripetal force is not a fundamental force (https://www.khanacademy.org/science/physics/centripetal-force-and-gravitation/centripetal-forces/a/science/cosmology-and-astronomy/universe-scale-topic/light-fundamental-forces/v/four-fundamental-forces), but just a label given to the net force which causes an object to move in a circular path. The tension force in the string of a swinging tethered ball and the gravitational force keeping a satellite in orbit are both examples of centripetal forces. Multiple individual forces can even be involved as long as they add up (by vector addition) to give a net force towards the center of the circular path.

Starting with Newton's 2ⁿᵈ law (https://www.khanacademy.org/science/physics/centripetal-force-and-gravitation/centripetal-forces/a/science/physics/forces-newtons-laws/newtons-laws-of-motion/a/what-is-newtons-second-law) :

a=Fma = \frac{F}{m}a=m
F​a, equals, start fraction, F, divided by, m, end fraction


and then equating this to the centripetal acceleration,

v2r=Fm\frac{v^2}{r} = \frac{F}{m}r
v2​=m
F​start fraction, v, start superscript, 2, end superscript, divided by, r, end fraction, equals, start fraction, F, divided by, m, end fraction


We can show that the centripetal force FCF_CFC​F, start subscript, C, end subscript has magnitude

Fc=mv2rF_c = \frac{mv^2}{r}Fc​=r
mv2​F, start subscript, c, end subscript, equals, start fraction, m, v, start superscript, 2, end superscript, divided by, r, end fraction


and is always directed towards the center of the circular path. Equivalently, if ω\omegaωomega is the angular velocity (https://www.khanacademy.org/science/physics/centripetal-force-and-gravitation/centripetal-forces/a/science/physics/torque-angular-momentum/torque-tutorial/v/relationship-between-angular-velocity-and-speed) then because v=rωv=r\omegav=rωv, equals, r, omega,

Fc=mrω2F_c = m r \omega^2Fc​=mrω2



Like i said, we're all saying the same thing, we're just using different terms and maybe perhaps focusing on seperate components of the phenomena..
Pam