Climb rate is a function of excess power, whereas glide ratio is a function of lift against drag as established by angle of attack. The lift to drag ratio varies with the AoA, which generally in light airplanes we establish by establishing an airspeed...a general approximation of AoA, but not a direct indication.
The glide ratio depends, then, on the airspeed we select, as well as the way the airplane is configured, and flown. An airplane flown at 65 knots will have a different glide than an airplane with 10% flaps extended at 65 knots, and different yet from an airplane flown slightly out of rig or out of "coordination" with or without flaps, etc. Further, the glide ratio depends on the energy absorption of the propeller, and the drag thereof; an airplane with a windmilling propeller glides farther and differently than an airplane with a stopped propeller, and different yet from an airplane being operated at a "zero thrust" setting.
Additionally, the two glides may be made with respect to "best" conditions; one will be maximum range, or the farthest glide, the other with minimum sink; decreased glide ratio and distance, but also decreased rate of descent and a longer time to reach the ground...as well as a reduced vertical impact rate if the same glide speed is maintained to impact.
Lift:drag ration is equal to glide ratio. If your best lift:drag ratio was 3:1 you'd never get airborne in, for example, a 1100 kg aircraft with 160 hp.
If you put the following in Google (it sorts out all the units) "160 hp / 75 kt" it tells you that the maximum thrust from perfect transmission of 160 hp at 75 kts is 3,313 N. Maximum lift would be three times this, 9,919 N. The force just to hold up a 1100 kg aircraft is 10,791 N.
That's incorrect, both regarding lift, and regarding thrust. In particular, one cannot equate the horsepower output of the engine with thrust, especially without specific information regarding propeller (pitch, fixed, constant speed, etc), propeller efficiency, propeller slippage, atmospheric conditions, propeller RPM, torque, airspeed, and so forth. Additionally, the engine never provides "perfect transmission." Further, climb is a function of excess thrust beyond that required to sustain level flight for a given equivilent airspeed and aircraft configuration. Further still, lift is a function of configuration and angle of attack, not engine power or thrust imparted by the propeller to the airstream.
You stipulated a force (in Newtons) which presumably represents the thrust you've calculated required to sustain level flight in a light airplane. Without having addressed the aircraft type, airspeed, weight, and other pertinent conditions, you simply can't throw out a number suggesting how much power is required, because no other information is given. What you have there is wild guesswork. Lift required to sustain flight is the weight of the aircraft plus down load, in a simple model.
You've confused yourself somewhat by attempting to come up with a thrust value in the first place, further by attempting to multiply it by three to equate a theoretical glide ratio (it doesn't work that way), and by introducing thrust into a glide equation in the first place. Moreover, an aircraft which glides 3:1 at L/Dmax doesn't require three times the thrust to fly, or four times the thrust to fly. You're attempting to impose the thrust value you've arbitrarily determined against what you perceive to the the value of the drag (which isn't known, and can't be directly determined strictly based on the glide ratio)...glide ratio is not the same as L/D ratio, and varies disproportionately as L/D is varied with configuration and AoA.
But it sounds good on the surface view.
You are correct, however, in that some airplanes have higher glide ratios than others. The Katana, or some versions, have glide ratios in excess of 14:1. Sailplanes can be very high...60:1. The U-2 wrings out about 28:1. The Cessna 150 and the Concorde both shared about the same number, around 7 to 8:1.
The cessna 150 has a sea level gross power to weight ratio of 1:16...sixteen pounds per one horsepower, though this is rated power and the engine produces substantially less with an increase in altitude, as well as lower propeller efficiency, etc. This isn't particularly relevant when discussing glide ratio, however, as previously discussed.
Again, however, the specific glide ratio for a given airplane under a given set of conditions really isn't important; the space shuttle has a dismal glide ratio, yet manages to hit it's mark each time, and the glide isn't nearly as important as the landing at the end. Additionally, unless one is far from a suitable forced landing site, then maximizing one's glide is really irrelevant, and minimum sink with a decreased glide ratio may become more important to establish communications, attempt an engine re-start, configure the aircraft or personnel on board for a forced landing, etc.