There isn't an exact gradient and there will always be the potential for wind. This is why they put wheel chocks when parking aircraft - at least those who want their planes to stay where they were parked.

Too many variable to give an "exact" answer. Static friction of the wheel bearings would be one, followed by interference from the brakes, temperature of the tyres, friction between tyres and ground surface, the surface itself ( concrete or steel or something very hard will be less than flexible blacktop paving) pressure in the tyres etc etc.

You see "strongmen" contests pulling big planes so clearly not much is needed to get them moving relative to their weight. go to 1:26 in this one https://www.youtube.com/watch?v=B-4NuNeIk3Q

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

where's this question coming from ? Why do you want to know the "exact" gradient (obviously dependent of tire pressure, friction, etc) ??

another day in paradise, or is paradise one day closer ?

Hmmmmm…

To expand slightly on what others have stated. Even though aircraft are heavy and tires are small... inflation pressures are remarkably high so that heavy aircraft have relatively small tire bulging/drag... and the wheels have very high precision roller bearings packed with grease. These design aspects alone are intended to minimize tire/wheel rolling friction. I have seen a couple of mechanics move a 40,000# jet with just a 'little sweat' [on dead-level surfaces]

A gradient is built into all large parking/apron/taxiways, simply for necessary rain/slush-water drainage.

As I recall, runways have a 'slight crown'... higher on the centerline and slightly lower on the edges [like most roads/freeways] for rain/slush-water drainage to the sides [water stagnation on a runway is bad news].

The only mandatory gradient of 'dead level' that I know of [~0+/-5-minute Deg, all orientations, as memory serves me poorly], is on parking/maintenance 'pads' intended for...

Outdoor aircraft jacking for maintenance or structural alignment inspections... under strictly enforced weather conditions.

Compass calibration... on compass-rose pads... under strictly enforced weather conditions.

Parking pads, under a open 'flow-thru' parking rain-shelter.

You have not been in maintenance, for real, until you've witnessed...

[A] An aircraft slowly rolling towards the edge of a parking apron and the keystone cops trying to stop it with chocks up to the last possible moment to prevent something bad happening. Most aircraft are balanced to a point just forward of the Main Gear tire contact point... so can easily tip-up/backwards onto the tail-cone/feathers... under many circumstances.

[B] An aircraft 'jumping' off one-or-more jack-pads, when elevated... bad things happen.

Regards, Wil Taylor
o Trust - But Verify!
o We believe to be true what we prefer to be true. [Unknown]
o For those who believe, no proof is required; for those who cannot believe, no proof is possible. [variation,Stuart Chase]
o Unfortunately, in science what You 'believe' is irrelevant. ["Orion", Homebuiltairplanes.com forum]

As you can see above we're going to get into the weeds on specifics.

If it's not perfectly flat, it can move is the conservative answer. Even then chocks and or chain it anyway... because reality.

Definitely going to be a civil engineer/code question.

If you're the guy writing the code... find a recent airport project of similar scale to your project, look up who the engineer/architect of record is and start making calls to them and the contractors who built the place. There is a guy who drives a white truck with yellow flashing lights on it that knows the answer.

My favorite tipping cause is heavy snow accumulation on the tail feathers. Just picturing that one critical snowflake that makes the difference drifting down to a soft landing and then comes the glacially slow tilt, unnoticed in the dark and freezing cold, until the ugly light of morning exposes the WTF.

But I can certainly understand the amazement when a runaway plane has its nose wheel pop over a hastily thrown chock.

I am just wondering if a grade of 1% in the longitudinal direction on a smooth concrete surface where no wind is guaranteed (like the inside of a hanger) will be enough to cause the typical airplane in one of the standard categories to start rolling. How about the FAA maximum allowable running grade of 0.8% in the first and last quarter of a runway, but inside a hangar? How about a 0.5% grade (limit for most light rail parking tracks), or even a 0.2%-0.25% longitudinal grade (limit for most railroads for vehicle storage tracks), also indoors on smooth concrete?

In other words, to make it simple, what are the typical values of net coefficient of friction for the wheel bearings and tires (and possibly also brakes that might be purposely designed to drag imperceptibly ever-so-slightly even when disengaged, which is standard for automobiles) combined for the following categories of aircraft (when they were new out of the factory) on a smooth concrete surface (such as indoors)? The categories are:

1. small piston-engined 2-to-3-row plane (such as Cessna 172)

2. turboprop minibus-sized 2-per-row airliner

3. turboprop bus-sized 2+2 per-row airliner

4. narrow-body 3+3 per-row jet airliner (such as Airbus A320 and Boeing 737)

5. mid-size wide-body jet airliner (such as Boeing 787 Dreamliner and Airbus A330)

6. large wide-body jet airliner (such as Boeing 777, Airbus A350, and Airbus A340), and

7. jumbo jet airliner (such as Boeing 747 and Airbus A380)

This is why I don't mind flying aircraft, but am terrified of bridges and dams.

Same user asked a very similar question in the Automotive Driveline section.

Explain yourself.

OK, Kwan Kok Ko… [Korean?]

Some math is appropriate/necessary for this discussion.

A 1-degree slope will translate to a small thrust vector.

TAN or SIN 1.000-Degree are virtually identical = 0.01745

Example of 'gravity thrust' due to a 1.000-Deg slope... EXAMPLE ONLY... for a 100,000 [pounds or Kilos static weight]

so...

0.01745 X 100,000 [pounds or Kilos] = 1745 [pounds or Kilos] gravity thrust for a 1.000-Deg slope-thrust vector.

NOW, factor this slope vector from wheel-tire-rolling orientation, around 90-deg to wheel-tire-side-load orientation [0-to-90], in 1-Degree increments.
NOTE1. This assumes 'perfectly still air'.

Try this simple math for any aircraft.

NOW...

Add in the effects of 'wind-drag loading' and this problem gets pretty hairy.
NOTE2. Determine wind [drag] forces on a 'static aircraft', 0.0000-deg slope. Wind orientation can be from any compass direction. Airframe wind-drag forces will vary dramatically, depending on 360-Deg wind-orientation to the airframe.

See what we've been talking about?

Regards, Wil Taylor
o Trust - But Verify!
o We believe to be true what we prefer to be true. [Unknown]
o For those who believe, no proof is required; for those who cannot believe, no proof is possible. [variation,Stuart Chase]
o Unfortunately, in science what You 'believe' is irrelevant. ["Orion", Homebuiltairplanes.com forum]

Interesting thought, if an aircraft has been sitting for a couple of days, are the tires still round, i.e does the first rotation of the tire require the same energy as the second rotation (unlikely as the rubber will have warmed fractionally). But Wind effects will be the wild card that wrecks the insurance rate, well until a human gets near a power leaver.
https://youtu.be/MeGlm_2da5M

Correct, that's called flatspotting, and is due to migration of the fibres in the layup through the semifluid rubber layers. This is why cars are shipped at 50 psi, because the assumption is they'll be siting around for a while.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

ok, more info, less "exact" but still the question is phrased badly.

Is the coefficient of friction going to depend on the class of airplane ?
or upon the weight of the airplane, the ground pressure area of the tires (which probably accounts for the weight), the type of concrete surface, the thread and wear of the tires, the "greaseiness" and/or wetness of the surface, the type of tire, the pressure of the tire ? the CBR of the surface ??

Again, why do you want this ??

another day in paradise, or is paradise one day closer ?

It's not a coefficient of friction really, it's rolling resistance. It is roughly proportional to weight but is dependent on tire construction, tire pressure, ground profile, ground softness (why not just put trays of kitty litter in each parking bay) and presumably phase of the moon.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

This isn't something which is calcuable IMHO. You will need to do some tests on somewhere truly flat with no wind and a calibrated force meter. The will be a peak static force followed by lower rolling resistance. Probably needs 10 tests on each aircraft type to find the lowest force to initiate movement.

Then you can calculate slope based on weight.

Please let us know when you've done it!

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.