FLT CREW OF CORPORATE JET FAILED TO MAKE CROSSING RESTRICTION AND FAILED TO ADVISE ATC IN TIME.

Narrative

A STRONG TAILWIND COMPONENT OF 50 KTS HAD PREPARED US FOR THE NEED TO DES IMMEDIATELY WHEN ANY XING RESTRICTION WAS GIVEN. OUR GND SPD WAS OVER 530 KTS. LEVEL AT FL270 THE CTLR ASKED US TO CROSS 50 W OF EEY AT AND MAINTAIN 16000'. AT THAT TIME WE WERE 72 MI W OF EEY. WE TOLD HIM WE PROBABLY COULD NOT MAKE THE RESTRICTION. HE TOLD US TO KEEP HIM ADVISED IF WE WEREN'T GOING TO MAKE IT. WE DO NOT HAVE VNAV; BUT WE DO USE SOME SIMPLE FORMULAS TO CALCULATE OUR VERT NAV PROBS. I TOLD THE CAPT WE COULDN'T MAKE IT; BUT HE DIDN'T RESPOND UNTIL WE WERE 10 MI FROM THE XING RESTRICTION. I TOLD ATC AND ATC CAME BACK WITH; 'YEAH; I COULD SEE THAT YOU WEREN'T GOING TO MAKE IT.' IF WE HAD REDUCED PWR TO FLT IDLE THRUST AND EXTENDED THE SPD BRAKES; AND DESCENDED AT MAXIMUM MACH WE COULD HAVE MADE THIS RESTRICTION. BUT; THAT IS AN ACCURATE DESCRIPTION FROM OUR FLT MANUAL OF AN EMER DES. IN THIS CASE WE MISSED THE RESTRICTION BY 1500'. EVIDENTLY THERE WAS NO TFC CONFLICT; MERELY AN AIRSPACE CONFLICT WHERE ATC HAD PROMISED TO DELIVER US AT AN ARR GATE AT A CERTAIN ALT AND WE WEREN'T ABLE TO DELIVER ON THE PROMISE. IT IS INCORRECT FOR ATC TO EXPECT DES RATES IN EXCESS OF 4000 FPM; IE EMER DESCENTS IN OUR NORMAL OPERATIONS; BUT WE ARE SEEING MORE AND MORE OF THIS TYPE OF SUBTLE REQUEST FROM ATC. I SUSPECT THAT TO AVOID THIS WOULD REQUIRE MORE PLANNING ON THE PART OF ATC OR A RESTRICTION ON THE AMOUNT OF TFC TRYING TO USE THE AIRSPACE.