I read a paperback book of short stories. One of the short stories was about time travel using an airplane, but the time travel was restricted to going forward in time. This resulted in a statue of them being erected.
I read a paperback book of short stories.
The story you're looking for is "The World of the Red Sun", a novelette by Clifford D. Simak, originally published in Wonder Stories, December 1931, available at the Internet Archive. You must have read it in a paperback edition of Before the Golden Age, an anthology edited by Isaac Asimov. Does any of these covers look familiar? Maybe this one, if it was an American edition.
One of the short stories was about time travel using an airplane,
Now Harl Swanson and Bill Kressman were out in the time stream. There had been a gasp of amazement from the crowd, on the street, which had seen the giant tri-motored plane suddenly disappear into thin air.
Harl crouched over the instrument board. His straining ears could distinguish the wheezy mutterings of the three motors as, despite the elaborate precautions taken to safeguard them, the inexorable fingers of absolute zero clutched at their throbbing metal.
This was a dangerous way, but the only safe way. Had they remained on the surface to plunge into the time stream they might have halted to find themselves and their machine buried by shifting earth; they might have found a great building over them, they might have found a canal covering them. Here in the air they were safe from all that might occur beneath them in the passing centuries through which they sped at an almost unbelievable pace. They were being fairly hurled through time.
Furthermore, the great machine would serve as a means of travel in that future day when they would roll out of the time stream back into space again. Perhaps it might serve as a means of escape, for there was no foreknowledge to tell them what they might expect a few thousand years in the future.
but the time travel was restricted to going forward in time.
"It is impossible to reverse time. You cannot travel back to your own age. I have no idea of what will occur if you attempt it, but I do know it is impossible. We of this age knew travel into the future was possible, but we lacked the technique to try it. Under the rule of Golan-Kirt there was no material progress, only a steady degeneration. We know that it is impossible to reverse time. We, as a people, beg you not to attempt it."
This resulted in a statue of them being erected.
"Bill," he spoke scarcely above a whisper, "am I seeing things?"
Before him, set on the sands of the arena, only a few yards from the plane, was a statue of heroic size, a statue of himself and Bill.
Even from where he stood he could read the inscription, carved in the white stone base of the statue in characters which closely resembled written English.
Slowly, haltingly, he read it aloud, stumbling over an occasional queer character.
"Two men, Harl Swanson, and Bill Kressman, came out of time to kill Golan-Kirt and to free the race."
Below it he saw other characters.
"They may return."
"Bill," he sobbed, "we haven't traveled back in time. We have traveled further into the future. Look at that stone--eroded, ready to crumble to pieces. That statue has stood there for thousands of years!"
Bill slumped back into his seat, his face ashen, his eyes staring.
"The old man was right," he screamed. "He was right. We'll never see the twentieth century again."