any pilots here who can answer a question?

You should have thought about that before you took off.

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, if there were a situation where a plane took off with one side fuel tank empty or significantly less full than the other, would it cause problems on takeoff due to weight/balance?

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Yes, it would cause significant problems

Yes, it would be a problem. Transport category aircraft have limitations on fuel imbalances. Fuel is a checklist item on every turbine plane I’ve ever flown(not just the presence of fuel, obviously, but the distribution of it). Maybe on the recips too, I haven’t flown one of those in a while.

Here's the reason I ask---I was telling someone about a flight I took about 9 years ago. The plane taxied down the runway, began to take off, and it seemed to make a hard left dip, then corrected right and leveled off, but at a very low altitude. Stopped climbing. We continued flying a very low altitude and several scary minutes later the pilot came on and told us we were returning to the airport. We flew around for a bit at this low altitude and then landed back at the same airport where we started. I'm not a good flyer to begin with, I take xanax so for sure my memory of the facts could be called into question, but after we landed and SAT ON THE PLANE FOR AN HOUR, (that is a fact, not clouded memory) the pilot came on the PA system and explained what was going on. As best as my foggy memory is, I'm pretty certain the pilot told us that prior to takeoff the fuel gauges registered full, but as soon as we took off, one of them dropped down to zero (or whatever) and they thought they had a faulty gauge but in reality the gauge was correct. Is that possible? I took it to mean that the tank wasn't in fact full and we were off balance. But in recounting this story to someone the other day they said they didn't think that was likely--that A) those things are checked before flight and B) planes can fly just fine with fuel imbalances and that it probably WAS just a faulty gauge.

I don't know...but that take off was definitely different from any other I have ever experienced.

Some do, some don’t. The C-130H can’t. I think the J model can. Just a couple of examples.

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Don't large planes have pumps that can move fuel back and forth between the different fuel tanks to trim the plane during flight? If the pilot took off with poorly trimmed tanks, couldn't they just move fuel and keep going?

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But if one tank was in fact empty, there wouldn’t have been enough fuel to get to their destination.

Dunno, but I got a CSB.

I was 16 and headed for my check ride in a Piper Warrior, which has low-wing tanks. You are supposed to switch from right tank to left tank every so often to keep the weight even between one side and the other. .

I pretty much ran the FBO, so I could fuel it as I chose. And I knew that the examiner who would check me out and either grant or deny my license was HUGE.

So to maintain roll balance, I had underfilled the right tank. He immediately noticed and asked me if I was aware.

Me: Yes sir.

Him: And that's ok?

Me: Avgas is 6 pounds a gallon. The right tank is 10 gallons lower than the left, and you outweigh me by about ninety pounds, sir. Accounting for the moment arm, ten gallons is about right.

Him: Well done, son.

I passed with flying colors.

Same thing almost happened to me. We started taxiing towards the runway and ended up turning around and going back to the gate. After parking for awhile a couple guys came and started putting more fuel in the wing.

I have a picture of them filling it up somewhere.

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if you put a slide rule to it you can take off and land with one wing tank full and the other side empty

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I’ve assumed this for a while. Ask a 130 FE about it though, and they’ll guarantee you will die.

Crossfeed. Doesn’t do much good as you realize passing thru V1 though.