On Rav Hershel Schachter’s method of tying with techelet

The majority of our techelet customers opt to have us tie the techelet strings according to the Arizal, Rambam, Sefer HaChinuch, Vilna Gaon or the Raavad. We also get plenty of orders for techelet tied like all-white tzitzit, according to the Ashkenazi or Sephardic customs. We discourage the latter, because those customs were developed in the absence of techelet and don’t make much sense with blue.
We rarely get requests for techelet tied according to Rav Hershel Schachter, but this week we’re working on a techelet order to be tied according to his approach.
If you take a look here you’ll see that Rav Schachter acknowledges that you can run into trouble with his shita because the strings are typically not long enough, so by the time you’re done with all the tying, you no longer have 2/3 of the length loose, which is required דרבנן.
עשות לכה”פ ז’ חוליות, ולעשות בין כל חוליא וחוליא קשר גמור של קשר ע”ג קשר, (כמנהגנו בזה”ז, דמ”ט נשנה את זה), ובכל חוליא יהי’ מינימום של ג’ כריכות (וכמבואר שם בגמ’ לעיל – וכמה שיעור חוליא, כדי שיכרוך וישנה וישלש.) ובודאי אם יעשה ז’ חוליות, ובכל אחת ז’ כריכות, יצא בזה לכו”ע, אך הרבה פעמים אין החוטים די-ארוכים לעשות מ”ט כריכות יחד עם ט”ז קשרים (כלומר, ח’ פעמים קשר ע”ג קשר, וכנ”ל), ולכתחילה מן הנכון שיהא חלק הכריכות כשליש מאורך החוטים, וחלק הענף שני שלישים. אכן אם יעשה לכה”פ החוליא הראשונה עם ז’ כריכות, ושאר החוליות עם ג’ כריכות, ירויח בזה במקצת, דמעיקר הדין סגי בחוליא אחת לעיכובא, והוספת ד’ הכריכות הנוספות שבחוליא הראשונה לא יגרום למעט כ”כ את אורך החוטים.
To solve the problem, he says you can tie the first section with seven windings and then the next six sections with just three windings. (Our tzitzit tie-er is pretty resourceful, and if memory serves, last time we tied Rav Schachter he managed to do seven sections of seven and still preserve the 1/3 to 2/3 ratio.)
The idea of the compromise solution is like as follows: Among the various different areas of dispute regarding techelet tying, there’s the question of what comprises a “chulya.” The Raavad says a chulya is seven windings, while all the other poskim say it’s three. Rav Schachter notes that מעיקר הדין one chulya makes your tzitzit kosher דאורייתא (i.e. one double knot, one section of windings and a second double knot), so if you make that first chulya according to the Raavad, you’ve got at least one proper chulya and the remaining chulyot are good according to the other poskim besides the Raavad.
If you click here and search for “Schachter” you’ll see that the Ptil Tekhelet Association suggests using that option if necessary.
Rav Mois Navon of the Ptil Tekhelet Association seems to be somewhat at odds with Rav Schachter’s tying method.
“R. Schachter holds that Ashkenazim should follow Tosafot with regard to the Tosafot opinion of the number of strings – i.e., Ashkenazim, according to R. Schachter, should use two blue and two white strings on each corner.  However, when discussing the method of tying, he believes that everyone (Ashkenazim and Sefaradim alike) should use the method put forth by the Rambam. Thus, confusion number one is due to the fact that R. Schachter’s method is really the combination of two methods for two separate issues concerning the one mitzvah of tzitzit – i.e., number of strings like Tosafot, method of tying like Rambam. Confusion number two arises from R. Schachter’s reading of the Rambam as opposed to the tradition the Yemenites (Teimanim) carry.  The Rambam explains, in very general terms, to make a hulya of three wraps, make a knot, give some distance and make the next hulya, etc. (Hil. Tzitz. 1:7 – see here).  The Yemenites have a tradition for tying according to the Rambam which they have preserved for centuries, for they have used it even for tying only white (as prescribed by the Rambam) – this method is shown in my diagram for the Rambam (see here).  R. Schachter, on the other hand, read the Rambam and said, ‘[T]he simplest knot I know is a double knot, and that also produces the space between hulyot defined by the Rambam.’ [T]his I know from personal conversations between R. Schachter and members of our Amuta (organization).”
Elsewhere Rav Navon also writes that he doesn’t approve of mixing and matching approaches, i.e. following one opinion regarding the number of blue strings and another opinion regarding how to go about tying them.