Expanding range of RF sender (FS1000)
From a theoretical perspective, (from my Ham radio days about 50 years ago) the ideal antenna is one where the Inductive and Capacitive Reactance cancel out, leaving pure resistance.  If that pure resistance matches the internal resistance on the transmitter side, the maximum amount of power is transferred to the antenna and radiated into space. An SWR meter is usually used to measure the forward vs. reflected power between the transmitter and antenna.  A standing wave ratio of 1:1, the ideal, means that the final amplifier, VT1 in this example, is matched to the antenna.  At other ratios the power that isn't transmitted is dissipated as heat on the collector of the transistor instead.  Measuring these values in a low-power setting like this would be very difficult.  Hence the recommendation that you would be best to use some multiple of a quarter-wavelength for the legs of your antenna.  That way, as is illustrated in the antenna graphs, the "electric waves" stand on the wire like a plucked guitar string and you end up feeding the antenna at a point where the load appears purely resistive.  At longer lengths the load appears inductive; shorter, capacitive. If shorter, you can slightly compensate for that with an inductor, called a base loading coil, which will help with matching, but will not really help with radiation.  You can find more practical info in the ARRL Antenna Book. 

I appreciate you posting the schematic.  I'm just starting to work with these cheap 433 MHz transmitter/receiver pairs.  I have found that they generate harmonics everywhere along the spectrum.  Harmonics are wasted energy, which is probably why their range is so bad.  Also, the receivers have a very broad bandwidth to accommodate the variation in the transmitter crystals.  This makes them subject to interference not just from other transmitters, but just about every key fob, garage door opener and radio-controlled toy out there.